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
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
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
This study explores the implementation of computed tomography(CT)reconstruction and simulation techniques for patient-specific valves,aiming to dissect the mechanical attributes of calcified valves within transcathete...This study explores the implementation of computed tomography(CT)reconstruction and simulation techniques for patient-specific valves,aiming to dissect the mechanical attributes of calcified valves within transcatheter heart valve replacement(TAVR)procedures.In order to facilitate this exploration,it derives pertinent formulas for 3D multi-material isogeometric hyperelastic analysis based on Hounsfield unit(HU)values,thereby unlocking foundational capabilities for isogeometric analysis in calcified aortic valves.A series of uniaxial and biaxial tensile tests is executed to obtain an accurate constitutive model for calcified active valves.To mitigate discretization errors,methodologies for reconstructing volumetric parametric models,integrating both geometric and material attributes,are introduced.Applying these analytical formulas,constitutive models,and precise analytical models to isogeometric analyses of calcified valves,the research ascertains their close alignment with experimental results through the close fit in displacement-stress curves,compellingly validating the accuracy and reliability of the method.This study presents a step-by-step approach to analyzing themechanical characteristics of patient-specific valves obtained fromCT images,holding significant clinical implications and assisting in the selection of treatment strategies and surgical intervention approaches in TAVR procedures.展开更多
The objective of this research was to determine the mechanical parameter from EVA foam and also investigate its behavior by using Blatz-Ko,Neo-Hookean,Mooney model and experimental test.The physical characteristic of ...The objective of this research was to determine the mechanical parameter from EVA foam and also investigate its behavior by using Blatz-Ko,Neo-Hookean,Mooney model and experimental test.The physical characteristic of EVA foam was also evaluated by scanning electron microscopy(SEM).The results show that Blatz-Ko and Neo-Hookean model can fit the curve at 5%and 8%strain,respectively.The Mooney model can fit the curve at 50%strain.The modulus of rigidity evaluated from Mooney model is 0.0814±0.0027 MPa.The structure of EVA foam from SEM image shows that EVA structure is a closed cell with homogeneous porous structure.From the result,it is found that Mooney model can adjust the data better than other models.This model can be applied for mechanical response prediction of EVA foam and also for reference value in engineering application.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
With slidable cross-links along the polymer strands,topological gels can adjust their network topology in response to the imposed loads.As reported in experimental studies from the literature,the unique cross-linking ...With slidable cross-links along the polymer strands,topological gels can adjust their network topology in response to the imposed loads.As reported in experimental studies from the literature,the unique cross-linking strategy and the distinct deformation mechanism result in a peculiar multiaxial behavior with minimal strain-coupling between different principal directions at relatively low cross-linking concentrations.This paper presents an element-free modelling of the topological gels focusing on their nonlinear stress–strain behavior under general biaxial extension.Specifically,conditions of uniaxial stretching and the three types of biaxial deformation,i.e.,equibiaxial stretching,pure shear deformation,and“two-step”biaxial deformation are investigated.The numerical stress–strain curves for these conditions are compared against those from the literature.展开更多
This paper proposes a new type of radial expansion mechanism by adopting the scissor type telescopic design for intestinal robot to meet the requirements of the intestinal robot’s movement and residence in the intest...This paper proposes a new type of radial expansion mechanism by adopting the scissor type telescopic design for intestinal robot to meet the requirements of the intestinal robot’s movement and residence in the intestinal tract.The robot’s maximum expansion radius is up to 25mm,which can well adapt to the intestinal tract with different diameters.At first,the mathematical model of the scissors-type telescopic mechanism(STM)is established to further study its dynamics characteristics by theoretical analysis and simulation.Then,in order to study the coupling effect between the STM and intestinal wall,the strain-energy function of Fung-type is used to establish the constitutive model of intestinal wall.Moreover,aimed at solving the non-convergence problem caused by the selection of material parameters in general Fung-type model,the restrictions for selecting material parameters were given by using positive definite matrix theory.Furthermore,the motion coupling characteristics between the mechanism and intestinal wall were analyzed by using the finite element method.The result shows that if the expansion radius of the STM exceeds a certain value,the intestinal wall may reach its deformation limit,which means that the maximum rotating angle of the three-claw butterfly disc of STM can be decided based on the maximum deformation stress of the intestinal wall.Therefore,it provides a design basis for formulating a reasonable expansion radius in mechanism control to avoid damage to the intestinal wall.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(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 Natural Science Foundation of China(Project Nos.52075340 and 61972011)the Shanghai Special Research Project on Aging Population and Maternal and Child Health(Project No.2020YJZX0106).
文摘This study explores the implementation of computed tomography(CT)reconstruction and simulation techniques for patient-specific valves,aiming to dissect the mechanical attributes of calcified valves within transcatheter heart valve replacement(TAVR)procedures.In order to facilitate this exploration,it derives pertinent formulas for 3D multi-material isogeometric hyperelastic analysis based on Hounsfield unit(HU)values,thereby unlocking foundational capabilities for isogeometric analysis in calcified aortic valves.A series of uniaxial and biaxial tensile tests is executed to obtain an accurate constitutive model for calcified active valves.To mitigate discretization errors,methodologies for reconstructing volumetric parametric models,integrating both geometric and material attributes,are introduced.Applying these analytical formulas,constitutive models,and precise analytical models to isogeometric analyses of calcified valves,the research ascertains their close alignment with experimental results through the close fit in displacement-stress curves,compellingly validating the accuracy and reliability of the method.This study presents a step-by-step approach to analyzing themechanical characteristics of patient-specific valves obtained fromCT images,holding significant clinical implications and assisting in the selection of treatment strategies and surgical intervention approaches in TAVR procedures.
基金supported by grants funded by Department of Mechanical Engineering,Faculty of Engineering,Chiang Mai University and the Graduate School of Chiang Mai University.
文摘The objective of this research was to determine the mechanical parameter from EVA foam and also investigate its behavior by using Blatz-Ko,Neo-Hookean,Mooney model and experimental test.The physical characteristic of EVA foam was also evaluated by scanning electron microscopy(SEM).The results show that Blatz-Ko and Neo-Hookean model can fit the curve at 5%and 8%strain,respectively.The Mooney model can fit the curve at 50%strain.The modulus of rigidity evaluated from Mooney model is 0.0814±0.0027 MPa.The structure of EVA foam from SEM image shows that EVA structure is a closed cell with homogeneous porous structure.From the result,it is found that Mooney model can adjust the data better than other models.This model can be applied for mechanical response prediction of EVA foam and also for reference value in engineering application.
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.
基金supported by the National Natural Science Foundation of China(12002247)the Natural Science Foundation of Hubei Province(2018CFB129)the Fundamental Research Funds for the Central Universities of China(WUT:2016IVA022 and WUT:2021IVB013).
文摘With slidable cross-links along the polymer strands,topological gels can adjust their network topology in response to the imposed loads.As reported in experimental studies from the literature,the unique cross-linking strategy and the distinct deformation mechanism result in a peculiar multiaxial behavior with minimal strain-coupling between different principal directions at relatively low cross-linking concentrations.This paper presents an element-free modelling of the topological gels focusing on their nonlinear stress–strain behavior under general biaxial extension.Specifically,conditions of uniaxial stretching and the three types of biaxial deformation,i.e.,equibiaxial stretching,pure shear deformation,and“two-step”biaxial deformation are investigated.The numerical stress–strain curves for these conditions are compared against those from the literature.
基金the Research Project of Traditional Chinese Medicine of Shanghai Health Committee(No.2020JP012)the Pujiang Talents’Project of Shanghai(No.20PJ1406600)the National Natural Science Foundation of China(No.61673271)。
文摘This paper proposes a new type of radial expansion mechanism by adopting the scissor type telescopic design for intestinal robot to meet the requirements of the intestinal robot’s movement and residence in the intestinal tract.The robot’s maximum expansion radius is up to 25mm,which can well adapt to the intestinal tract with different diameters.At first,the mathematical model of the scissors-type telescopic mechanism(STM)is established to further study its dynamics characteristics by theoretical analysis and simulation.Then,in order to study the coupling effect between the STM and intestinal wall,the strain-energy function of Fung-type is used to establish the constitutive model of intestinal wall.Moreover,aimed at solving the non-convergence problem caused by the selection of material parameters in general Fung-type model,the restrictions for selecting material parameters were given by using positive definite matrix theory.Furthermore,the motion coupling characteristics between the mechanism and intestinal wall were analyzed by using the finite element method.The result shows that if the expansion radius of the STM exceeds a certain value,the intestinal wall may reach its deformation limit,which means that the maximum rotating angle of the three-claw butterfly disc of STM can be decided based on the maximum deformation stress of the intestinal wall.Therefore,it provides a design basis for formulating a reasonable expansion radius in mechanism control to avoid damage to the intestinal wall.
