A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying dom...A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying domain integrals.Trial function is constructed by using a radial basis function （RBF） coupled with a polynomial basis function,in which the shape function possesses the kronecker delta function property.So,additional treatment is not required for imposing essential boundary conditions.Governing equations of impact problems are established and solved node by node by using an explicit time integration algorithm in a local domain,which is very similar to that of the collocation method except that numerical integration can be implemented over local domain in the present method.Numerical results for several examples show that the present method performs well in dealing with the dynamic impact problem of hyperelastic material.展开更多
In this paper,the choice and parametrisation of finite deformation polyconvex isotropic hyperelastic models to describe the behaviour of a class of defect-free monocrystalline metal materials at the molecular level is...In this paper,the choice and parametrisation of finite deformation polyconvex isotropic hyperelastic models to describe the behaviour of a class of defect-free monocrystalline metal materials at the molecular level is examined.The article discusses some physical,mathematical and numerical demands which in our opinion should be fulfilled by elasticity models to be useful.A set of molecular numerical tests for aluminium and tungsten providing data for the fitting of a hyperelastic model was performed,and an algorithm for parametrisation is discussed.The proposed models with optimised parameters are superior to those used in non-linear mechanics of crystals.展开更多
Granular materials exhibit complex macroscopic mechanical behaviors closely related to their microscalemicrostructural features.Traditional macroscopic phenomenological elasto-plastic models,however,usually have compl...Granular materials exhibit complex macroscopic mechanical behaviors closely related to their microscalemicrostructural features.Traditional macroscopic phenomenological elasto-plastic models,however,usually have complex formulations and lack explicit relations to these microstructural features.To avoid these limitations,this study proposes a micromechanics-based softening hyperelastic model for granular materials,integrating softening hyperelasticity withmicrostructural insights to capture strain softening,critical state,and strain localization behaviors.The model has two key advantages:(1)a clear conceptualization,straightforward formulation,and ease of numerical implementation(via Abaqus UMAT subroutine in this study);(2)explicit incorporation of micro-scale features(e.g.,contact stiffness,particle size,porosity)to reveal their influences on macroscopic responses.An isotropic directional distribution density of contacts and three specific microstructures are considered,and their softening hyperelastic constitutive modulus tensors are explicitly derived.By introducing a softening factor and critical failure energy density,the model can describe geomaterial behaviors,simulating residual strength,X-shaped shear bands,and strain localization evolution.Numerical validations in comparison with themacro-scale hyperelastic model,Abaqus Drucker-Prager model,and the experiment confirm its accuracy.Parametric studies reveal critical dependencies:a normal to tangential contact stiffness ratio of 2-8(depending on stiffness magnitude),an internal length of 2-4 mm to ensure shear band formation,and a critical failure energy density(≤10 kJ/m^(3))to trigger strain softening and localization.Influences of the specific microstructures on strain localization and softening are investigated.The model also shows mesh independence due to the introduction of an internal length.The model’s applicability is further demonstrated by slope stability analysis,capturing slip surface evolution,and load-displacement characteristics.This study develops a robust microstructure-aware hyperelastic framework to describe the mechanical behaviors of granular materials,providing multiscale insights for geotechnical engineering applications.展开更多
The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimiz...The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimizing their design.However,conventional numerical methods can face challenges with the non-linearities inherent in hyperelasticity and the complex spatial variations in FGMs.This paper presents a novel hybrid numerical approach combining Physics-Informed Neural Networks(PINNs)with Finite Element Method(FEM)derived data for the robust analysis of thick-walled,axisymmetric,heterogeneous,hyperelastic pressure vessels with elliptical geometries.A PINN framework incorporating neo-Hookean constitutive relations is developed in MATLAB.To enhance training efficiency and accuracy,the PINN’s loss function is augmented with displacement data obtained from high-fidelity FEM simulations performed in ANSYS.The methodology is rigorously validated by comparing PINN-predicted displacement and von Mises stress fields against ANSYS benchmarks for various scenarios of FGMconfigurations(with material properties varying according to a power law)subjected to internal and external pressurization.The results demonstrate excellent agreement between the proposed hybrid PINN-FEMapproach and conventional FEMsolutions across all test cases,accurately capturing complex deformation patterns and stress concentrations.This study highlights the potential of data-augmented PINNs as an effective and accurate computational tool for tackling complex solid mechanics problems involving non-linearmaterials and significant heterogeneity,offering a promising avenue for future research in engineering design and analysis.展开更多
The meniscus plays an important role in the biomechanical function of the knee joint,but knee osteoarthritis(OA)deteriorates the mechanical properties of the meniscus.Thus understanding the mechanical behaviour of the...The meniscus plays an important role in the biomechanical function of the knee joint,but knee osteoarthritis(OA)deteriorates the mechanical properties of the meniscus.Thus understanding the mechanical behaviour of the OA meniscus is very important.This study aimed to assess the quasi-static nonlinear mechanical behaviours of the three zones of the OA meniscus by a proposed meso-indentation method,and further to investigate its nonlinear mechanical responses under the stance.Four pairs of menisci were harvested from OA patients during total knee arthroplasty.One pair of the menisci was first used for the histological analysis.Binocular fringe projection technology was then employed to reconstruct the morphology of the other three pairs of the menisci.Subsequently,a meso-indentation method was proposed to characterize the nonlinear behaviors of the meniscus zones,moreover,the hyperelastic model(HEM)together with the Hertz’s elastic model(EM)was used to fit the indentation force-depth curves of the meniscus zones.Furthermore,the fitted HEM and EM materials parameters were used to simulate the mechanical response of the meniscus in the stance by two simplified meniscus models.The results showed that the type Ⅲ collagen widely existed in the OA menisci,and the red-white zone exhibited the best mechanical performance,and the 3-term Mooney-Rivlin model was the best descriptor for the nonlinear mechanical characterization of the three zones.Moreover,the stress or strain distributions of the simplified meniscus models differed significantly between the HEM and EM under the stance,and the EM underestimated the mechanical behaviours of the meniscus.The current work generally provides a novel testing method to study the nonlinear mechanical behaviour of soft biological materials,and is specifically helpful to understand the nonlinear mechanical behaviour of the OA meniscus for which the HEM should be used in the meniscus-related biomechanical studies.展开更多
Dozens of hyperelastic models have been formulated and have been extremely handy in understanding the complex mechanical behavior of materials that exhibit hyperelastic behavior(characterized by large nonlinear elasti...Dozens of hyperelastic models have been formulated and have been extremely handy in understanding the complex mechanical behavior of materials that exhibit hyperelastic behavior(characterized by large nonlinear elastic deformations that are completely recoverable)such as elastomers,polymers,and even biological tis-sues.These models are indispensable in the design of complex engineering com-ponents such as engine mounts and structural bearings in the automotive and aerospace industries and vibration isolators and shock absorbers in mechanical systems.Particularly,the problem of vibration control in mechanical system dy-namics is extremely important and,therefore,knowledge of accurate hyperelastic models facilitates optimum designs and the development of three‐dimensional finite element system dynamics for studying the large and nonlinear deformation beha-vior.This review work intends to enhance the knowledge of 15 of the most com-monly used hyperelastic models and consequently help design engineers and scientists make informed decisions on the right ones to use.For each of the models,expressions for the strain‐energy function and the Cauchy stress for both arbitrary loading assuming compressibility and each of the three loading modes(uniaxial tension,equibiaxial tension,and pure shear)assuming incompressibility are pro-vided.Furthermore,the stress–strain or stress–stretch plots of the model's pre-dictions in each of the loading modes are compared with that of the classical experimental data of Treloar and the coefficient of determination is utilized as a measure of the model's predictive ability.Lastly,a ranking scheme is proposed based on the model's ability to predict each of the loading modes with minimum deviations and the overall coefficient of determination.展开更多
With the increasing and refined applications of silicone rubber devices in the biomedical field,it is of great significance to accurately describe and predict the mechanical behavior of them under large deformation.Th...With the increasing and refined applications of silicone rubber devices in the biomedical field,it is of great significance to accurately describe and predict the mechanical behavior of them under large deformation.This paper finds that after con-sidering the influence of higher-order shear strain on the normal stress,the Poynting effect in ribbed silicone rubber tubes with certain cross-sectional shapes exhibits a new phenomenon―a non-monotonic trend between axial deformation and twist angle.This paper develops a nonlinear finite element program for simulating large deformations of hyperelastic materials,and studies the Poynting effect in ribbed circular tubes of twisted silicone rubber.The results show that in the ribbed circular tubes with a porosity between 12% and 40%(with the number of ribs ranging from 12 to 26),there appears a normal to reverse conversion of the Poynting effect,that is,the axial extension ratio first decreases and then increases during a monotonic loading process,indicating that the influence of higher-order shear strain on normal stress cannot be ignored when the cross-sectional shape is complex.Especially in ribbed circular tubes with about 20% porosity,a substantial change of axial normal strain from−0.035% to 0.035% can be achieved within a twist angle range of 180°.Based on this,the quantitative influence of higher-order shear strain on normal stress is studied.These research results provide a theoretical basis for accurately controlling the axial expansion and contraction of twisted parts and indicate that a normal to reverse conversion of the Poynting effect can be implemented by designing the cross-sectional shape under certain conditions.展开更多
The inflation tests of rubbery membranes have been widely employed as an efficient method to characterize the stress response as biaxial loading states.However,most of the previous theoretical works have employed clas...The inflation tests of rubbery membranes have been widely employed as an efficient method to characterize the stress response as biaxial loading states.However,most of the previous theoretical works have employed classic hyperelastic models to analyze the deformation behaviors of inflated membranes.The classic models have been demonstrated to lack the ability to capturing the biaxial deformation of rubbers.To address this issue,we have combined the analytical method and the finite element simulation to investigate the deformation response of soft membranes with different constitutive relationships.For the analytical method,the governing ordinary differential equations have been set up for the boundary value problem of inflation tests and further solved using the shooting method.The analytical results are consistent with those obtained from finite element simulation.The results show that the deformation belongs to the unequal biaxial condition rather than the equi-biaxial state unless a neo-Hookean model is adopted.We also perform a parameter study using the extended eight-chain model,which shows that a change in different parameters affects the mechanical response of inflation tests variously.This work may shed light on the future experimental characterization of soft materials using inflation experiments.展开更多
The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break...The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.展开更多
Rubber-like materials that are commonly used in structural applications are modelled using hyperelastic material models.Most of the hyperelastic materials are nearly incompressible,which poses challenges,i.e.,volumetr...Rubber-like materials that are commonly used in structural applications are modelled using hyperelastic material models.Most of the hyperelastic materials are nearly incompressible,which poses challenges,i.e.,volumetric locking during numerical modelling.There exist many formulations in the context of the finite element method,among which the mixed displacementpressure formulation is robust.However,such a displacement-pressure formulation is less explored in meshfree methods,which mitigates the problem associated with mesh distortion during large deformation.This work addresses this issue of alleviating volumetric locking in the element-free Galerkin method(EFGM),which is one of the popular meshfree methods.A two-field mixed variational formulation using the perturbed Lagrangian approach within the EFGM framework is proposed for modelling nearly incompressible hyperelastic material models,such as Neo-Hookean and Mooney-Rivlin.Taking advantage of the meshless nature of the EFGM,this work introduces a unique approach by randomly distributing pressure nodes across the geometry,following specific guidelines.A wide spectrum of problems involving bending,tension,compression,and contact is solved using two approaches of the proposed displacement-pressure node formulation involving regular and irregular pressure node distribution.It is observed that both approaches give accurate results compared to the reference results,though the latter offers flexibility in the pressure nodal distribution.展开更多
Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method （MLPG） is presented. A material configuration based the nonlinear MLPG formulat...Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method （MLPG） is presented. A material configuration based the nonlinear MLPG formulation is introduced for the large deformation analysis of both path-dependent and path-independent materials. The supports of the MLS approximation functions cover the same sets of nodes during material deformation, thus the shape function needs to be computed only in the initial stage. The multiplicative hyperelasto-plastic constitutive model is adopted to avoid objective time integration for stress update in large rota- tion. With this constitutive model, the computational formulations for path-dependent and path-independent materials become identical. Computational efficiency of the nonlinear MLPG method is discussed and optimized in several aspects to make the MLPG an O（N） algorithm. The numerical examples indicate that the MLPG method can solve large deformation problems accurately. Moreover, the MLPG computations enjoy better convergence rate than the FEM under very large particle distortion.展开更多
Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed bas...Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed based on the multiresolution design strategy(MRDS)and the additive hyperelasticity technique(AHT),taking into account the geometric nonlinearity and material nonlinearity.The MR-NTO strategy is established in the framework of the solid isotropic material with penalization(SIMP)method,while the Neo-Hookean hyperelastic material model characterizes the material nonlinearity.The coarse analysis grid is employed for finite element(FE)calculation,and the fine material grid is applied to describe the material configuration.To alleviate the convergence problem and reduce sensitivity calculation complexity,the software ANSYS coupled with AHT is utilized to perform the nonlinear FE calculation.A strategy for redistributing strain energy is proposed during the sensitivity analysis,i.e.,transforming the strain energy of the analysis element into that of the material element,including Neo-Hooken and second-order Yeoh material.Numerical examples highlight three distinct advantages of the proposed method,i.e.,it can(1)significantly improve the computational efficiency,(2)make up for the shortcoming that NTO based on AHT may have difficulty in convergence when solving the NTO problem,especially for 3D problems,(3)successfully cope with high-resolution 3D complex NTO problems on a personal computer.展开更多
Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear ...Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems,to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials.By applying the adaptive refinement capability of T-splines during the iteration process of analysis,the numerical simulation accuracy of the nonlinear model could be increased dramatically.The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be easily incorporated into existing nonlinear finite element codes.In addition,T-splines show great superiority of modeling complex geometries especially when the model is irregular and with hole features.Several numerical examples have been tested to validate the accuracy and convergence of the proposed method.The obtained results are compared with those from NURBS-based isogeometric analysis and commercial software ABAQUS.展开更多
Soft materials with semi-linear strain energy function can be used as smart transformation media to manipulate elastic waves via finite pre-deformation. However, the intrinsic cons train ts involved in such materials ...Soft materials with semi-linear strain energy function can be used as smart transformation media to manipulate elastic waves via finite pre-deformation. However, the intrinsic cons train ts involved in such materials limit the shapes of t ransformation devices to very sim - pie cases. In this work, combining theoretical and numerical analyses, we report an approach of achieving the in-plane elastodynamic cloak with arbitrary shape. We demonstrate that with the appropriate out-of^plane st retch applied on the semi-linear material, cloaking effec t can be achieved for both P- and SV-waves in the symmetrie plane of a 3D domain, and the performance of the cloak with arbitrary cross section can be guaranteed for relatively small in-plane rot at ion. In addition, we propose an empirical formula to predic t the deformation limit of the cloaks with semi-linear materials. This work may stimulate the experimental research on softmatter- based transformation devices. Potential applications can be anticipated in nondestructive testing, structure impact protection, biomedical imaging and soft robotics.展开更多
Elastomers are used in numerous engineering applications such as sealing components, it is therefore important to devise a method that can accurately predict elastomers’ response to load. Many applications that emplo...Elastomers are used in numerous engineering applications such as sealing components, it is therefore important to devise a method that can accurately predict elastomers’ response to load. Many applications that employ the use of these materials subject them to a nonlinear large strain;therefore the simple Hooke’s law is not sufficient to describe their material behaviour. This paper presents an approach to obtain material properties of elastomer under compression loading, based on hyperelastic strain formulation, through experimental test and finite element modelling. The paper focuses on the isotropic incompressible behaviour exhibited by elastomers, and obtains strain energy functions that satisfy the characteristic properties of a hyperelastic model. Data obtained from compression test on a nitrile rubber (NBR) specimen were used as material input into ABAQUS®—a finite element analysis software. A least square fitting technique was used to determine the coefficients of various stable hyperelastic models, based on Drucker’s stability criteria within the software. The strain energy functions obtained concentrate on material parameters which are related to physical quantities of the material molecular network they are subjected to in practical application. The approach benefits from mathematical simplicity, and possesses the property of the deformation mode dependency. Furthermore, a model validation procedure using a step-by-step method for parameters estimation is explained. The work herein is a nonlinear finite element modelling process that leads to an optimal solution and can be employed not only for elastomeric seals, but also for similar engineering assets.展开更多
This paper proposes a constitutive law and a method for characterizing highly preloaded viscoelastic materials subjected to linear （small-amplitude） vibrations. A multiplicative non-separable variables law has been ...This paper proposes a constitutive law and a method for characterizing highly preloaded viscoelastic materials subjected to linear （small-amplitude） vibrations. A multiplicative non-separable variables law has been suggested to model the behavior that depends on both stretch and time/frequency. This approach allows splitting the intricate combined test performed simultaneously on both stretch and frequency, generally in a limited experimental domain up to 100 Hz, into two independent tests. Thus, on one hand, the dynamic complex modulus dependent on frequency alone is evaluated on the basis of vibration tests in a large experimental domain up to 100 kHz. On the other hand, energetic parameters are determined from a quasi-static hyperelastic tensile test. The complex modulus, dependent on both stretch and frequency, is then deduced from the results acquired from uncoupled investigations. This work shows that, in extension, the elastic modulus increases with increasing stretch, and the loss factor decreases with increasing stretch; while, in compression, around the material undeformed state, the modulus increases as the stretch increases till a certain value of compression stretch （upturn point depending on material characteristics）, and then the modulus decreases as the stretch increases. Globally, preload rigidifies materials but reduces their damping property. These results closely match a well-known observation in solid mechanics.展开更多
One can compute the final deformation of a known geometry under specific boundary conditions using the constitutive laws of mechanics that describe their stress strain behavior.In such cases the initial geometry is kn...One can compute the final deformation of a known geometry under specific boundary conditions using the constitutive laws of mechanics that describe their stress strain behavior.In such cases the initial geometry is known,and all operators mapping the deformation are defined on the reference domain.However,there are situations in which the final configuration of a deformation might be known but not the initial.The inverse formulation allows one to determine the initial geometry of a domain,given its final deformation state,the material behavior law and a set of boundary conditions.In the present work we propose a method to reconstruct the mesoscale geometry of a textile based on its mechanical response during compaction.To do so,stress boundary conditions are acquired by means of a pressuresensitive film.By adopting an appropriate material law,the thickness and width information of the yarns are deduced from the pressure field experienced by the compacted textile.Unlike 3 D scanning techniques such as-CT,the proposed method can be applied on any domain size,allowing long-range variability to be captured.To the best of the authors’knowledge,there are no previous works that use a pressure-sensitive film on a large domain to capture the input data for a shape reconstruction.This example application serves as a demonstration of a methodology which could be applied to other classes of materials.展开更多
A constitutive model to describe the behavior of rubber from low to high strain rates is presented.For loading,the primary hyperelastic behavior is characterized by the six parameter Ogden’s strain-energy potential o...A constitutive model to describe the behavior of rubber from low to high strain rates is presented.For loading,the primary hyperelastic behavior is characterized by the six parameter Ogden’s strain-energy potential of the third order.The rate-dependence is captured by the nonlinear second order BKZ model using another five parameters,having two relaxation times.For unloading,a single parameter model has been presented to define Hysteresis or continuous damage,while Ogden’s two term model has been used to capture Mullin’s effect or discontinuous damage.Lastly,the Feng-Hallquist failure surface dictates the ultimate failure for element deletion.The proposed model can accurately predict the response of rubber using a limited set of experimental data.The model has been validated here for the case of rubber but can be extended to a wide range of polymers.展开更多
This paper deals with a stochastic approach based on the principle of the maximum entropy to investigate the effect of the parameter random uncertainties on the arterial pressure. Motivated by a hyperelastic, anisotro...This paper deals with a stochastic approach based on the principle of the maximum entropy to investigate the effect of the parameter random uncertainties on the arterial pressure. Motivated by a hyperelastic, anisotropic, and incompressible constitutive law with fiber families, the uncertain parameters describing the mechanical behavior are considered. Based on the available information, the probability density functions are attributed to every random variable to describe the dispersion of the model parameters. Numerous realizations are carried out, and the corresponding arterial pressure results are compared with the human non-invasive clinical data recorded over a mean cardiac cycle. Furthermore, the Monte Carlo simulations are performed, the convergence of the probabilistic model is proven. The different realizations are useful to define a reliable confidence region, in which the probability to have a realization is equM to 95%. It is shown through the obtained results that the error in the estimation of the arterial pressure can reach 35% when the estimation of the model parameters is subjected to an uncertainty ratio of 5%. Finally, a sensitivity analysis is performed to identify the constitutive law relevant parameters for better understanding and characterization of the arterial wall mechanical behaviors.展开更多
基金supported by the National Natural Science Foundation of China(No.10902038)
文摘A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying domain integrals.Trial function is constructed by using a radial basis function （RBF） coupled with a polynomial basis function,in which the shape function possesses the kronecker delta function property.So,additional treatment is not required for imposing essential boundary conditions.Governing equations of impact problems are established and solved node by node by using an explicit time integration algorithm in a local domain,which is very similar to that of the collocation method except that numerical integration can be implemented over local domain in the present method.Numerical results for several examples show that the present method performs well in dealing with the dynamic impact problem of hyperelastic material.
文摘In this paper,the choice and parametrisation of finite deformation polyconvex isotropic hyperelastic models to describe the behaviour of a class of defect-free monocrystalline metal materials at the molecular level is examined.The article discusses some physical,mathematical and numerical demands which in our opinion should be fulfilled by elasticity models to be useful.A set of molecular numerical tests for aluminium and tungsten providing data for the fitting of a hyperelastic model was performed,and an algorithm for parametrisation is discussed.The proposed models with optimised parameters are superior to those used in non-linear mechanics of crystals.
基金supported by the National Natural Science Foundation of China through grant numbers 12002245 and 12172263the Science and Technology Research Program of Chongqing Municipal Education Commission through grant number KJQN202300742+1 种基金the National Natural Science Foundation of ChongqingMunicipality through grant number CSTB2025NSCQ-GPX0841Chongqing Jiaotong University through grant number F1220038.
文摘Granular materials exhibit complex macroscopic mechanical behaviors closely related to their microscalemicrostructural features.Traditional macroscopic phenomenological elasto-plastic models,however,usually have complex formulations and lack explicit relations to these microstructural features.To avoid these limitations,this study proposes a micromechanics-based softening hyperelastic model for granular materials,integrating softening hyperelasticity withmicrostructural insights to capture strain softening,critical state,and strain localization behaviors.The model has two key advantages:(1)a clear conceptualization,straightforward formulation,and ease of numerical implementation(via Abaqus UMAT subroutine in this study);(2)explicit incorporation of micro-scale features(e.g.,contact stiffness,particle size,porosity)to reveal their influences on macroscopic responses.An isotropic directional distribution density of contacts and three specific microstructures are considered,and their softening hyperelastic constitutive modulus tensors are explicitly derived.By introducing a softening factor and critical failure energy density,the model can describe geomaterial behaviors,simulating residual strength,X-shaped shear bands,and strain localization evolution.Numerical validations in comparison with themacro-scale hyperelastic model,Abaqus Drucker-Prager model,and the experiment confirm its accuracy.Parametric studies reveal critical dependencies:a normal to tangential contact stiffness ratio of 2-8(depending on stiffness magnitude),an internal length of 2-4 mm to ensure shear band formation,and a critical failure energy density(≤10 kJ/m^(3))to trigger strain softening and localization.Influences of the specific microstructures on strain localization and softening are investigated.The model also shows mesh independence due to the introduction of an internal length.The model’s applicability is further demonstrated by slope stability analysis,capturing slip surface evolution,and load-displacement characteristics.This study develops a robust microstructure-aware hyperelastic framework to describe the mechanical behaviors of granular materials,providing multiscale insights for geotechnical engineering applications.
文摘The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimizing their design.However,conventional numerical methods can face challenges with the non-linearities inherent in hyperelasticity and the complex spatial variations in FGMs.This paper presents a novel hybrid numerical approach combining Physics-Informed Neural Networks(PINNs)with Finite Element Method(FEM)derived data for the robust analysis of thick-walled,axisymmetric,heterogeneous,hyperelastic pressure vessels with elliptical geometries.A PINN framework incorporating neo-Hookean constitutive relations is developed in MATLAB.To enhance training efficiency and accuracy,the PINN’s loss function is augmented with displacement data obtained from high-fidelity FEM simulations performed in ANSYS.The methodology is rigorously validated by comparing PINN-predicted displacement and von Mises stress fields against ANSYS benchmarks for various scenarios of FGMconfigurations(with material properties varying according to a power law)subjected to internal and external pressurization.The results demonstrate excellent agreement between the proposed hybrid PINN-FEMapproach and conventional FEMsolutions across all test cases,accurately capturing complex deformation patterns and stress concentrations.This study highlights the potential of data-augmented PINNs as an effective and accurate computational tool for tackling complex solid mechanics problems involving non-linearmaterials and significant heterogeneity,offering a promising avenue for future research in engineering design and analysis.
基金supported by the National Nature Science Foundation of China(Grant Nos.32171307,12372307,12172089,61821002 and 82102567)the Basic Research Plan Natural Science Foundation of Jiangsu Province(Grant No.BK20232023)+1 种基金the Nature Science Foundation of Jiangsu Province(Grant No.BK20200144)the Postgraduate Research and Practice Innovation Program of Jiangsu Province(Grant No.5007032303).
文摘The meniscus plays an important role in the biomechanical function of the knee joint,but knee osteoarthritis(OA)deteriorates the mechanical properties of the meniscus.Thus understanding the mechanical behaviour of the OA meniscus is very important.This study aimed to assess the quasi-static nonlinear mechanical behaviours of the three zones of the OA meniscus by a proposed meso-indentation method,and further to investigate its nonlinear mechanical responses under the stance.Four pairs of menisci were harvested from OA patients during total knee arthroplasty.One pair of the menisci was first used for the histological analysis.Binocular fringe projection technology was then employed to reconstruct the morphology of the other three pairs of the menisci.Subsequently,a meso-indentation method was proposed to characterize the nonlinear behaviors of the meniscus zones,moreover,the hyperelastic model(HEM)together with the Hertz’s elastic model(EM)was used to fit the indentation force-depth curves of the meniscus zones.Furthermore,the fitted HEM and EM materials parameters were used to simulate the mechanical response of the meniscus in the stance by two simplified meniscus models.The results showed that the type Ⅲ collagen widely existed in the OA menisci,and the red-white zone exhibited the best mechanical performance,and the 3-term Mooney-Rivlin model was the best descriptor for the nonlinear mechanical characterization of the three zones.Moreover,the stress or strain distributions of the simplified meniscus models differed significantly between the HEM and EM under the stance,and the EM underestimated the mechanical behaviours of the meniscus.The current work generally provides a novel testing method to study the nonlinear mechanical behaviour of soft biological materials,and is specifically helpful to understand the nonlinear mechanical behaviour of the OA meniscus for which the HEM should be used in the meniscus-related biomechanical studies.
基金National Natural Science Foundation of China,Grant/Award Number:11772109。
文摘Dozens of hyperelastic models have been formulated and have been extremely handy in understanding the complex mechanical behavior of materials that exhibit hyperelastic behavior(characterized by large nonlinear elastic deformations that are completely recoverable)such as elastomers,polymers,and even biological tis-sues.These models are indispensable in the design of complex engineering com-ponents such as engine mounts and structural bearings in the automotive and aerospace industries and vibration isolators and shock absorbers in mechanical systems.Particularly,the problem of vibration control in mechanical system dy-namics is extremely important and,therefore,knowledge of accurate hyperelastic models facilitates optimum designs and the development of three‐dimensional finite element system dynamics for studying the large and nonlinear deformation beha-vior.This review work intends to enhance the knowledge of 15 of the most com-monly used hyperelastic models and consequently help design engineers and scientists make informed decisions on the right ones to use.For each of the models,expressions for the strain‐energy function and the Cauchy stress for both arbitrary loading assuming compressibility and each of the three loading modes(uniaxial tension,equibiaxial tension,and pure shear)assuming incompressibility are pro-vided.Furthermore,the stress–strain or stress–stretch plots of the model's pre-dictions in each of the loading modes are compared with that of the classical experimental data of Treloar and the coefficient of determination is utilized as a measure of the model's predictive ability.Lastly,a ranking scheme is proposed based on the model's ability to predict each of the loading modes with minimum deviations and the overall coefficient of determination.
基金supported by the National Natural Science Foundation of China(Grant Nos.52009107 and 11972285)the Youth Innovation Team Project of Shaanxi Provincial Department of Education(Grant No.21JP079).
文摘With the increasing and refined applications of silicone rubber devices in the biomedical field,it is of great significance to accurately describe and predict the mechanical behavior of them under large deformation.This paper finds that after con-sidering the influence of higher-order shear strain on the normal stress,the Poynting effect in ribbed silicone rubber tubes with certain cross-sectional shapes exhibits a new phenomenon―a non-monotonic trend between axial deformation and twist angle.This paper develops a nonlinear finite element program for simulating large deformations of hyperelastic materials,and studies the Poynting effect in ribbed circular tubes of twisted silicone rubber.The results show that in the ribbed circular tubes with a porosity between 12% and 40%(with the number of ribs ranging from 12 to 26),there appears a normal to reverse conversion of the Poynting effect,that is,the axial extension ratio first decreases and then increases during a monotonic loading process,indicating that the influence of higher-order shear strain on normal stress cannot be ignored when the cross-sectional shape is complex.Especially in ribbed circular tubes with about 20% porosity,a substantial change of axial normal strain from−0.035% to 0.035% can be achieved within a twist angle range of 180°.Based on this,the quantitative influence of higher-order shear strain on normal stress is studied.These research results provide a theoretical basis for accurately controlling the axial expansion and contraction of twisted parts and indicate that a normal to reverse conversion of the Poynting effect can be implemented by designing the cross-sectional shape under certain conditions.
基金supported by the National Natural Science Foundation of China(Grant Nos.12211530061 and 12321002)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LD22A020001)the 111 Project(Grant No.B21034).
文摘The inflation tests of rubbery membranes have been widely employed as an efficient method to characterize the stress response as biaxial loading states.However,most of the previous theoretical works have employed classic hyperelastic models to analyze the deformation behaviors of inflated membranes.The classic models have been demonstrated to lack the ability to capturing the biaxial deformation of rubbers.To address this issue,we have combined the analytical method and the finite element simulation to investigate the deformation response of soft membranes with different constitutive relationships.For the analytical method,the governing ordinary differential equations have been set up for the boundary value problem of inflation tests and further solved using the shooting method.The analytical results are consistent with those obtained from finite element simulation.The results show that the deformation belongs to the unequal biaxial condition rather than the equi-biaxial state unless a neo-Hookean model is adopted.We also perform a parameter study using the extended eight-chain model,which shows that a change in different parameters affects the mechanical response of inflation tests variously.This work may shed light on the future experimental characterization of soft materials using inflation experiments.
基金support from the National Natural Science Foundation of China(Nos.12102242 and 12172086)the Educational Foundation of Liaoning Province(No.JYTQN2023261)the Key R&D Program of Shandong Province of China(No.2022SFGC0801).
文摘The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.
基金supported by the DST-SERB and VSSC,ISRO of the project titled“Functionality Enhancement through Design and Development of Advanced Finite Element Algorithms for STR tools”under IMPRINT.IIC(IMP/2019/000276)scheme.
文摘Rubber-like materials that are commonly used in structural applications are modelled using hyperelastic material models.Most of the hyperelastic materials are nearly incompressible,which poses challenges,i.e.,volumetric locking during numerical modelling.There exist many formulations in the context of the finite element method,among which the mixed displacementpressure formulation is robust.However,such a displacement-pressure formulation is less explored in meshfree methods,which mitigates the problem associated with mesh distortion during large deformation.This work addresses this issue of alleviating volumetric locking in the element-free Galerkin method(EFGM),which is one of the popular meshfree methods.A two-field mixed variational formulation using the perturbed Lagrangian approach within the EFGM framework is proposed for modelling nearly incompressible hyperelastic material models,such as Neo-Hookean and Mooney-Rivlin.Taking advantage of the meshless nature of the EFGM,this work introduces a unique approach by randomly distributing pressure nodes across the geometry,following specific guidelines.A wide spectrum of problems involving bending,tension,compression,and contact is solved using two approaches of the proposed displacement-pressure node formulation involving regular and irregular pressure node distribution.It is observed that both approaches give accurate results compared to the reference results,though the latter offers flexibility in the pressure nodal distribution.
基金The project supported by the National Natural Science Foundation of China (10472051). The English text was polished by Keren Wang
文摘Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method （MLPG） is presented. A material configuration based the nonlinear MLPG formulation is introduced for the large deformation analysis of both path-dependent and path-independent materials. The supports of the MLS approximation functions cover the same sets of nodes during material deformation, thus the shape function needs to be computed only in the initial stage. The multiplicative hyperelasto-plastic constitutive model is adopted to avoid objective time integration for stress update in large rota- tion. With this constitutive model, the computational formulations for path-dependent and path-independent materials become identical. Computational efficiency of the nonlinear MLPG method is discussed and optimized in several aspects to make the MLPG an O（N） algorithm. The numerical examples indicate that the MLPG method can solve large deformation problems accurately. Moreover, the MLPG computations enjoy better convergence rate than the FEM under very large particle distortion.
基金supported by the National Natural Science Foundation of China(Grant Nos.11902085 and 11832009)the Science and Technology Association Young Scientific and Technological Talents Support Project of Guangzhou City(Grant No.SKX20210304)the Natural Science Foundation of Guangdong Province(Grant No.2021Al515010320).
文摘Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization(NTO).To this end,a multi-resolution nonlinear topology optimization(MR-NTO)method is proposed based on the multiresolution design strategy(MRDS)and the additive hyperelasticity technique(AHT),taking into account the geometric nonlinearity and material nonlinearity.The MR-NTO strategy is established in the framework of the solid isotropic material with penalization(SIMP)method,while the Neo-Hookean hyperelastic material model characterizes the material nonlinearity.The coarse analysis grid is employed for finite element(FE)calculation,and the fine material grid is applied to describe the material configuration.To alleviate the convergence problem and reduce sensitivity calculation complexity,the software ANSYS coupled with AHT is utilized to perform the nonlinear FE calculation.A strategy for redistributing strain energy is proposed during the sensitivity analysis,i.e.,transforming the strain energy of the analysis element into that of the material element,including Neo-Hooken and second-order Yeoh material.Numerical examples highlight three distinct advantages of the proposed method,i.e.,it can(1)significantly improve the computational efficiency,(2)make up for the shortcoming that NTO based on AHT may have difficulty in convergence when solving the NTO problem,especially for 3D problems,(3)successfully cope with high-resolution 3D complex NTO problems on a personal computer.
基金support by the Natural Science Foundation of China(Project Nos.61972011 and 61572056).
文摘Nonlinear behaviors are commonplace in many complex engineering applications,e.g.,metal forming,vehicle crash test and so on.This paper focuses on the T-spline based isogeometric analysis of two-dimensional nonlinear problems including general large deformation hyperelastic problems and small deformation elastoplastic problems,to reveal the advantages of local refinement property of T-splines in describing nonlinear behavior of materials.By applying the adaptive refinement capability of T-splines during the iteration process of analysis,the numerical simulation accuracy of the nonlinear model could be increased dramatically.The Bézier extraction of the T-splines provides an element structure for isogeometric analysis that can be easily incorporated into existing nonlinear finite element codes.In addition,T-splines show great superiority of modeling complex geometries especially when the model is irregular and with hole features.Several numerical examples have been tested to validate the accuracy and convergence of the proposed method.The obtained results are compared with those from NURBS-based isogeometric analysis and commercial software ABAQUS.
基金National Natural Science Foundation of China (Grant Nos. 11472044, 11521062, 11602294, 11632003)the Chinese Universities Scientific Fund (Grant No. 2019TC134).
文摘Soft materials with semi-linear strain energy function can be used as smart transformation media to manipulate elastic waves via finite pre-deformation. However, the intrinsic cons train ts involved in such materials limit the shapes of t ransformation devices to very sim - pie cases. In this work, combining theoretical and numerical analyses, we report an approach of achieving the in-plane elastodynamic cloak with arbitrary shape. We demonstrate that with the appropriate out-of^plane st retch applied on the semi-linear material, cloaking effec t can be achieved for both P- and SV-waves in the symmetrie plane of a 3D domain, and the performance of the cloak with arbitrary cross section can be guaranteed for relatively small in-plane rot at ion. In addition, we propose an empirical formula to predic t the deformation limit of the cloaks with semi-linear materials. This work may stimulate the experimental research on softmatter- based transformation devices. Potential applications can be anticipated in nondestructive testing, structure impact protection, biomedical imaging and soft robotics.
文摘Elastomers are used in numerous engineering applications such as sealing components, it is therefore important to devise a method that can accurately predict elastomers’ response to load. Many applications that employ the use of these materials subject them to a nonlinear large strain;therefore the simple Hooke’s law is not sufficient to describe their material behaviour. This paper presents an approach to obtain material properties of elastomer under compression loading, based on hyperelastic strain formulation, through experimental test and finite element modelling. The paper focuses on the isotropic incompressible behaviour exhibited by elastomers, and obtains strain energy functions that satisfy the characteristic properties of a hyperelastic model. Data obtained from compression test on a nitrile rubber (NBR) specimen were used as material input into ABAQUS®—a finite element analysis software. A least square fitting technique was used to determine the coefficients of various stable hyperelastic models, based on Drucker’s stability criteria within the software. The strain energy functions obtained concentrate on material parameters which are related to physical quantities of the material molecular network they are subjected to in practical application. The approach benefits from mathematical simplicity, and possesses the property of the deformation mode dependency. Furthermore, a model validation procedure using a step-by-step method for parameters estimation is explained. The work herein is a nonlinear finite element modelling process that leads to an optimal solution and can be employed not only for elastomeric seals, but also for similar engineering assets.
文摘This paper proposes a constitutive law and a method for characterizing highly preloaded viscoelastic materials subjected to linear （small-amplitude） vibrations. A multiplicative non-separable variables law has been suggested to model the behavior that depends on both stretch and time/frequency. This approach allows splitting the intricate combined test performed simultaneously on both stretch and frequency, generally in a limited experimental domain up to 100 Hz, into two independent tests. Thus, on one hand, the dynamic complex modulus dependent on frequency alone is evaluated on the basis of vibration tests in a large experimental domain up to 100 kHz. On the other hand, energetic parameters are determined from a quasi-static hyperelastic tensile test. The complex modulus, dependent on both stretch and frequency, is then deduced from the results acquired from uncoupled investigations. This work shows that, in extension, the elastic modulus increases with increasing stretch, and the loss factor decreases with increasing stretch; while, in compression, around the material undeformed state, the modulus increases as the stretch increases till a certain value of compression stretch （upturn point depending on material characteristics）, and then the modulus decreases as the stretch increases. Globally, preload rigidifies materials but reduces their damping property. These results closely match a well-known observation in solid mechanics.
基金partially funded by Conseil Regional Pays de la Loire(grant number TEU29)。
文摘One can compute the final deformation of a known geometry under specific boundary conditions using the constitutive laws of mechanics that describe their stress strain behavior.In such cases the initial geometry is known,and all operators mapping the deformation are defined on the reference domain.However,there are situations in which the final configuration of a deformation might be known but not the initial.The inverse formulation allows one to determine the initial geometry of a domain,given its final deformation state,the material behavior law and a set of boundary conditions.In the present work we propose a method to reconstruct the mesoscale geometry of a textile based on its mechanical response during compaction.To do so,stress boundary conditions are acquired by means of a pressuresensitive film.By adopting an appropriate material law,the thickness and width information of the yarns are deduced from the pressure field experienced by the compacted textile.Unlike 3 D scanning techniques such as-CT,the proposed method can be applied on any domain size,allowing long-range variability to be captured.To the best of the authors’knowledge,there are no previous works that use a pressure-sensitive film on a large domain to capture the input data for a shape reconstruction.This example application serves as a demonstration of a methodology which could be applied to other classes of materials.
文摘A constitutive model to describe the behavior of rubber from low to high strain rates is presented.For loading,the primary hyperelastic behavior is characterized by the six parameter Ogden’s strain-energy potential of the third order.The rate-dependence is captured by the nonlinear second order BKZ model using another five parameters,having two relaxation times.For unloading,a single parameter model has been presented to define Hysteresis or continuous damage,while Ogden’s two term model has been used to capture Mullin’s effect or discontinuous damage.Lastly,the Feng-Hallquist failure surface dictates the ultimate failure for element deletion.The proposed model can accurately predict the response of rubber using a limited set of experimental data.The model has been validated here for the case of rubber but can be extended to a wide range of polymers.
文摘This paper deals with a stochastic approach based on the principle of the maximum entropy to investigate the effect of the parameter random uncertainties on the arterial pressure. Motivated by a hyperelastic, anisotropic, and incompressible constitutive law with fiber families, the uncertain parameters describing the mechanical behavior are considered. Based on the available information, the probability density functions are attributed to every random variable to describe the dispersion of the model parameters. Numerous realizations are carried out, and the corresponding arterial pressure results are compared with the human non-invasive clinical data recorded over a mean cardiac cycle. Furthermore, the Monte Carlo simulations are performed, the convergence of the probabilistic model is proven. The different realizations are useful to define a reliable confidence region, in which the probability to have a realization is equM to 95%. It is shown through the obtained results that the error in the estimation of the arterial pressure can reach 35% when the estimation of the model parameters is subjected to an uncertainty ratio of 5%. Finally, a sensitivity analysis is performed to identify the constitutive law relevant parameters for better understanding and characterization of the arterial wall mechanical behaviors.
