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
Nonlinear finite element analysis is widely used for structural optimization of the design and the reliability analysis of complex elastomeric components.However,high-precision numerical results cannot be achieved wit...Nonlinear finite element analysis is widely used for structural optimization of the design and the reliability analysis of complex elastomeric components.However,high-precision numerical results cannot be achieved without reliable strain energy functions(SEFs)of the rubber or rubber nanocomposite material.Although hyperelastic constitutive models have been studied for nearly 80 years,selecting one that accurately describes rubber's mechanical response is still a challenge.This work reviews 85 isotropic SEFs based on both the phenomenological theory and the micromechanical network theory proposed from the 1940s to 2019.A fitting algorithm which can realize the automatic fitting optimization and determination of the parameters of all SEFs reviewed is developed.The ability of each SEF to reproduce the experimental data of both the unfilled and highly filled rubber nanocomposite is quantitatively assessed based on a new proposed evaluation index.The top 30 SEFs for the unfilled rubber and the top 14 SEFs for the highly filled rubber nanocomposite are presented in the ranking lists.Finally,some suggestions on how to select an appropriate hyperelastic constitutive model are given,and the perspective on the future progress of constitutive models is summarized.展开更多
The spherical cavitated bifurcation for a hyperelastic solid sphere made of the incompressible Valanis-Landel material under boundary dead-loading is examined. The analytic solution for the bifurcation problem is obta...The spherical cavitated bifurcation for a hyperelastic solid sphere made of the incompressible Valanis-Landel material under boundary dead-loading is examined. The analytic solution for the bifurcation problem is obtained. The catastrophe and concentration of stresses are discussed. The stability of solutions is discussed through the energy comparison. And the growth of a pre-existing micro-void is also observed.展开更多
In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inn...In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.展开更多
The partial differential equation for isotropic hyperelastic constitutive models has been postulated and derived from the balance between stored energy and stress work done. The partial differential equation as a func...The partial differential equation for isotropic hyperelastic constitutive models has been postulated and derived from the balance between stored energy and stress work done. The partial differential equation as a function of three invariants has then been solved by Lie group methods. With geometric meanings of deformations, the general solution boils down to a particular three-term solution. The particular solution has been applied for several isotropic hyperelastic materials. For incompressible materials, vulcanized rubber containing 8% sulfur and Entec Enflex S4035A thermoplastic elastomer, three coefficients have been determined from uniaxial tension data and applied to predict the pure shear and equibiaxial tension modes. For a slightly compressible rubber material, the coefficients have also been extracted from the confined volumetric test data.展开更多
In this paper,a nonlinear wave equation with variable coefficients is studied,interestingly,this equation can be used to describe the travelling waves propagating along the circular rod composed of a general compressi...In this paper,a nonlinear wave equation with variable coefficients is studied,interestingly,this equation can be used to describe the travelling waves propagating along the circular rod composed of a general compressible hyperelastic material with variable cross-sections and variable material densities.With the aid of Lou’s direct method1,the nonlinear wave equation with variable coefficients is reduced and two sets of symmetry transformations and exact solutions of the nonlinear wave equation are obtained.The corresponding numerical examples of exact solutions are presented by using different coefficients.Particularly,while the variable coefficients are taken as some special constants,the nonlinear wave equation with variable coefficients reduces to the one with constant coefficients,which can be used to describe the propagation of the travelling waves in general cylindrical rods composed of generally hyperelastic materials.Using the same method to solve the nonlinear wave equation,the validity and rationality of this method are verified.展开更多
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
Primary objective of automobile seats is to offer adequate level of safety and comfort to the seated human occupant, primarily against vibration. Ideally, any sort of automotive seat is constructed by mechanical frame...Primary objective of automobile seats is to offer adequate level of safety and comfort to the seated human occupant, primarily against vibration. Ideally, any sort of automotive seat is constructed by mechanical framework, cushion, backrest and headrest. The frame structures are made of metallic alloys, while the cushion, backrest and headrest are made of polyurethane foam material. During the design phase of automotive seat, the greatest challenge is to assign realistic material properties to foam material;as it is non-linear in nature and exhibit hysteresis at low level stress. In this research paper, a car seat has been modelled in finite element environment by implementing both hyperelastic and viscoelastic material properties to polyurethane foam. The car seat has been excited with the loads due to car acceleration and human object and the effects of vibration in terms of vertical acceleration at different locations have been measured. The aims of this simulation study are to establish a car seat with the foam material properties as accurately as possible and provide a finite element set up of car seat to monitor the vertical acceleration responses in a reasonable way. The RMS acceleration values for headrest, backrest and cushion have been found to be 0.91 mm/sec2, 0.54 mm/sec2 and 0.47 mm/sec2, respectively, which showed that the car seat foam can effectively be modelled through combined hyperelastic and viscoelastic material formulations. The simulation outputs have been validated through real life testing data, which clearly indicates that this computerized simulation technique is capable of anticipating the acceleration responses at different car seat segments in a justified way.展开更多
Vascular diseases such as aneurysm,hemadostenosis,aortic dissection are the primary causes of people’s death around world.As a result,it is significant to improve our knowledge about them,which can help to treat the ...Vascular diseases such as aneurysm,hemadostenosis,aortic dissection are the primary causes of people’s death around world.As a result,it is significant to improve our knowledge about them,which can help to treat the disease.Measuring the hemodynamic factor like the blood pressure,the wall shear stress(WSS)and the oscillatory shear index(OSI)is,however,still beyond the capabilities of in-vivo measurement techniques.So the use of mathematical models and numerical simulations for the studies of the blood flow in arteries and,in general,of the cardiovascular system,both in physiological and pathological conditions,has received an increasing attention in the biomedical community during the last two decades.Indeed,such studies aims at enhancing the current knowledge of the physiology of the cardiovascular system,as well as providing reliable tools for the medical doctors to predict the natural course of pathologies and,possibly,the occurrence of cardiovascular accidents.The computational vascular fluid-structure interaction(FSI)methodology is a numerical simulation method which is used to explain the hemodynamic factors.The WSS on the luminal wall and the mechanical stress in the vascular wall are directly related to the location of the lesion,and the blood flow strongly interacts with the vascular wall motion.The arterial wall continually adapts to the charge of its mechanical environment(due to,for example,growth,atrophy,remodelling,repair,ageing,and disease)and consequently undergoes several irreversible processes.Primary acute mechanisms of vascularFSI numerical simulation seem to be associated with(1)the arterial histology and the patient-specific complex geometry,(2)the typical mechanical properties of the layer,(3)properties of the blood is assumed as Newtonian fluid or non-Newtonian fluid based on the scale ofthe diameter of a vessel,(4)residual stress in the zero-pressure configuration.The arterial system naturally function under permanent physiological loading conditions.Fung defined the residual stress and measured the opening angle which varies greatly along the aortic tree.Consequently,most of these systems never experience a stress-free state in their’service life’,so a stress and strain fields are present in any in vivo obtained patientspecific cardiovascular geometry.The residual stress always be ignored in FSI simulation or be assumed to equal zero,and the vivo patient-specific artery geometry is assumed as zero-pressure configuration.To define the in vivo stress state of artery,an inverse problem needs to be solved:the undeformed shape of a body or its stress state in its deformed state needs to be determined given the deformed configuration and the loads causing this deformation.The modular inverse elastostatics method is used to resolve the pressure-induced stress state for in vivo imaging based on cardiovascular modeling proposed by Peirlinck.Here,we build a living vessel FSI model based on 4 key factors.In order to get the universal simulation results,we focus on idealized geometries of the vessel that represent healthy(physiological)conditions of the cerebral vasculature.Blood can be assumed as the Newtonian fluid at this scale.The anisotropic hyperelastic constitutive law(Gasser-Holzapfel-Ogden)is used in zero-pressure configuration.Afterwards,we propose the material parameters for the different constitutive models and the computational configurations.We demonstrate the importance of introducing the residual stress into vascular blood flow modeling by performing a comparing zero-pressure configuration and no-resistance configuration.We get the conclusion that the zero-pressure status model has smaller displacement and larger stress distribution compared with no-resistance stress model.Hence,the methodology presented here will be particularly useful to study the mechanobiological processes in the healthy and diseased vascular wall.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
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
In the presenl paper. the finite deformation and stress analysis for a hyperelasticrectangular plate with a center void under a uniaxial extension is studied. In order toconsider the effect of the exijtence of the voi...In the presenl paper. the finite deformation and stress analysis for a hyperelasticrectangular plate with a center void under a uniaxial extension is studied. In order toconsider the effect of the exijtence of the void on the deformation and stress of theplate, the problem is reduced to the deformation and stress analysis for a hyperelusticannular plate and its approximate solution is obtained from the minimum potentialenergy principle. The growth of the cavitation iS also nunterically computed andanalysed.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
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
Some nonlinear dynamic properties of axisymmetric deformation are ex- amined for a spherical membrane composed of a transversely isotropic incompressible Rivlin-Saunders material. The membrane is subjected to periodic...Some nonlinear dynamic properties of axisymmetric deformation are ex- amined for a spherical membrane composed of a transversely isotropic incompressible Rivlin-Saunders material. The membrane is subjected to periodic step loads at its inner and outer surfaces. A second-order nonlinear ordinary differential equation approximately describing radially symmetric motion of the membrane is obtained by setting the thick- ness of the spherical structure close to one. The qualitative properties of the solutions are discussed in detail. In particular, the conditions that control the nonlinear periodic oscillation of the spherical membrane are proposed. In certain cases, it is proved that the oscillating form of the spherical membrane would present a homoclinic orbit of type ＂∞＂, and the amplitude growth of the periodic oscillation is discontinuous. Numerical results are provided.展开更多
The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility...The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility condition of the material. The solution was approximately obtained from the minimum potential energy principle. The growth of voids was discussed. One can see that an initial central circular-cylinder void becomes an elliptic-cylinder void, but an initial non-centeral circular-cylinder void becomes an elliptic-like cylinder void and the center of void has a shift. The stress distributions along the edges of voids were given and the phenomenon of stress concentration was observed. The influences of the distribution manner and size of voids, as well as the distance between them on the growth of voids were analyzed.展开更多
The e?ect of material anisotropy on the bifurcation for void formation in anisotropic compressible hyperelastic materials is examined. Numerical solutions are obtained in an anisotropic sphere, whose material is tra...The e?ect of material anisotropy on the bifurcation for void formation in anisotropic compressible hyperelastic materials is examined. Numerical solutions are obtained in an anisotropic sphere, whose material is transversely isotropic in the radial direction. It is shown that the bifur- cation may occur either to the right or to the left, depending on the degree of material anisotropy. The deformation and stress contribution in the sphere before cavitation are di?erent from those after cavitation. The stability of solutions is discussed through a comparison of energy.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(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the National Key Research and Development Program of China(2018YFB1502501)the National Natural Science Foundation of China(52003024).
文摘Nonlinear finite element analysis is widely used for structural optimization of the design and the reliability analysis of complex elastomeric components.However,high-precision numerical results cannot be achieved without reliable strain energy functions(SEFs)of the rubber or rubber nanocomposite material.Although hyperelastic constitutive models have been studied for nearly 80 years,selecting one that accurately describes rubber's mechanical response is still a challenge.This work reviews 85 isotropic SEFs based on both the phenomenological theory and the micromechanical network theory proposed from the 1940s to 2019.A fitting algorithm which can realize the automatic fitting optimization and determination of the parameters of all SEFs reviewed is developed.The ability of each SEF to reproduce the experimental data of both the unfilled and highly filled rubber nanocomposite is quantitatively assessed based on a new proposed evaluation index.The top 30 SEFs for the unfilled rubber and the top 14 SEFs for the highly filled rubber nanocomposite are presented in the ranking lists.Finally,some suggestions on how to select an appropriate hyperelastic constitutive model are given,and the perspective on the future progress of constitutive models is summarized.
文摘The spherical cavitated bifurcation for a hyperelastic solid sphere made of the incompressible Valanis-Landel material under boundary dead-loading is examined. The analytic solution for the bifurcation problem is obtained. The catastrophe and concentration of stresses are discussed. The stability of solutions is discussed through the energy comparison. And the growth of a pre-existing micro-void is also observed.
基金Project supported by the National Natural Science Foundation of China (Nos. 10872045 and 10772104)the Program for New Century Excellent Talents in University (No. NCET-09-0096)the Fundamental Research Funds for the Central Universities (No. DC10030104)
文摘In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.
文摘The partial differential equation for isotropic hyperelastic constitutive models has been postulated and derived from the balance between stored energy and stress work done. The partial differential equation as a function of three invariants has then been solved by Lie group methods. With geometric meanings of deformations, the general solution boils down to a particular three-term solution. The particular solution has been applied for several isotropic hyperelastic materials. For incompressible materials, vulcanized rubber containing 8% sulfur and Entec Enflex S4035A thermoplastic elastomer, three coefficients have been determined from uniaxial tension data and applied to predict the pure shear and equibiaxial tension modes. For a slightly compressible rubber material, the coefficients have also been extracted from the confined volumetric test data.
基金This work is supported by the National Natural Science Foundation of China(Nos.11672069,11702059,11232003,11672062)The Ph.D.Programs Foundation of Ministry of Education of China(No.20130041110050)+3 种基金the Research Startup Project Plan for Liaoning Doctors(No.20141119)the Fundamental Research Funds for the Central Universities(20000101)the Natural Science Foundation of Liaoning Province(No.20170540199)111 Project(B08014).
文摘In this paper,a nonlinear wave equation with variable coefficients is studied,interestingly,this equation can be used to describe the travelling waves propagating along the circular rod composed of a general compressible hyperelastic material with variable cross-sections and variable material densities.With the aid of Lou’s direct method1,the nonlinear wave equation with variable coefficients is reduced and two sets of symmetry transformations and exact solutions of the nonlinear wave equation are obtained.The corresponding numerical examples of exact solutions are presented by using different coefficients.Particularly,while the variable coefficients are taken as some special constants,the nonlinear wave equation with variable coefficients reduces to the one with constant coefficients,which can be used to describe the propagation of the travelling waves in general cylindrical rods composed of generally hyperelastic materials.Using the same method to solve the nonlinear wave equation,the validity and rationality of this method are verified.
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Primary objective of automobile seats is to offer adequate level of safety and comfort to the seated human occupant, primarily against vibration. Ideally, any sort of automotive seat is constructed by mechanical framework, cushion, backrest and headrest. The frame structures are made of metallic alloys, while the cushion, backrest and headrest are made of polyurethane foam material. During the design phase of automotive seat, the greatest challenge is to assign realistic material properties to foam material;as it is non-linear in nature and exhibit hysteresis at low level stress. In this research paper, a car seat has been modelled in finite element environment by implementing both hyperelastic and viscoelastic material properties to polyurethane foam. The car seat has been excited with the loads due to car acceleration and human object and the effects of vibration in terms of vertical acceleration at different locations have been measured. The aims of this simulation study are to establish a car seat with the foam material properties as accurately as possible and provide a finite element set up of car seat to monitor the vertical acceleration responses in a reasonable way. The RMS acceleration values for headrest, backrest and cushion have been found to be 0.91 mm/sec2, 0.54 mm/sec2 and 0.47 mm/sec2, respectively, which showed that the car seat foam can effectively be modelled through combined hyperelastic and viscoelastic material formulations. The simulation outputs have been validated through real life testing data, which clearly indicates that this computerized simulation technique is capable of anticipating the acceleration responses at different car seat segments in a justified way.
基金supported by the National Natural Science Foundation of China ( 11732001)
文摘Vascular diseases such as aneurysm,hemadostenosis,aortic dissection are the primary causes of people’s death around world.As a result,it is significant to improve our knowledge about them,which can help to treat the disease.Measuring the hemodynamic factor like the blood pressure,the wall shear stress(WSS)and the oscillatory shear index(OSI)is,however,still beyond the capabilities of in-vivo measurement techniques.So the use of mathematical models and numerical simulations for the studies of the blood flow in arteries and,in general,of the cardiovascular system,both in physiological and pathological conditions,has received an increasing attention in the biomedical community during the last two decades.Indeed,such studies aims at enhancing the current knowledge of the physiology of the cardiovascular system,as well as providing reliable tools for the medical doctors to predict the natural course of pathologies and,possibly,the occurrence of cardiovascular accidents.The computational vascular fluid-structure interaction(FSI)methodology is a numerical simulation method which is used to explain the hemodynamic factors.The WSS on the luminal wall and the mechanical stress in the vascular wall are directly related to the location of the lesion,and the blood flow strongly interacts with the vascular wall motion.The arterial wall continually adapts to the charge of its mechanical environment(due to,for example,growth,atrophy,remodelling,repair,ageing,and disease)and consequently undergoes several irreversible processes.Primary acute mechanisms of vascularFSI numerical simulation seem to be associated with(1)the arterial histology and the patient-specific complex geometry,(2)the typical mechanical properties of the layer,(3)properties of the blood is assumed as Newtonian fluid or non-Newtonian fluid based on the scale ofthe diameter of a vessel,(4)residual stress in the zero-pressure configuration.The arterial system naturally function under permanent physiological loading conditions.Fung defined the residual stress and measured the opening angle which varies greatly along the aortic tree.Consequently,most of these systems never experience a stress-free state in their’service life’,so a stress and strain fields are present in any in vivo obtained patientspecific cardiovascular geometry.The residual stress always be ignored in FSI simulation or be assumed to equal zero,and the vivo patient-specific artery geometry is assumed as zero-pressure configuration.To define the in vivo stress state of artery,an inverse problem needs to be solved:the undeformed shape of a body or its stress state in its deformed state needs to be determined given the deformed configuration and the loads causing this deformation.The modular inverse elastostatics method is used to resolve the pressure-induced stress state for in vivo imaging based on cardiovascular modeling proposed by Peirlinck.Here,we build a living vessel FSI model based on 4 key factors.In order to get the universal simulation results,we focus on idealized geometries of the vessel that represent healthy(physiological)conditions of the cerebral vasculature.Blood can be assumed as the Newtonian fluid at this scale.The anisotropic hyperelastic constitutive law(Gasser-Holzapfel-Ogden)is used in zero-pressure configuration.Afterwards,we propose the material parameters for the different constitutive models and the computational configurations.We demonstrate the importance of introducing the residual stress into vascular blood flow modeling by performing a comparing zero-pressure configuration and no-resistance configuration.We get the conclusion that the zero-pressure status model has smaller displacement and larger stress distribution compared with no-resistance stress model.Hence,the methodology presented here will be particularly useful to study the mechanobiological processes in the healthy and diseased vascular wall.
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.
文摘In the presenl paper. the finite deformation and stress analysis for a hyperelasticrectangular plate with a center void under a uniaxial extension is studied. In order toconsider the effect of the exijtence of the void on the deformation and stress of theplate, the problem is reduced to the deformation and stress analysis for a hyperelusticannular plate and its approximate solution is obtained from the minimum potentialenergy principle. The growth of the cavitation iS also nunterically computed andanalysed.
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.
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.
基金supported by the National Natural Science Foundation of China (Nos.10872045, 10721062,and 10772104)the Program for New Century Excellent Talents in University (No.NCET-09-0096)+1 种基金the Post-Doctoral Science Foundation of China (No.20070421049)the Fundamental Research Funds for the Central Universities (No.DC10030104)
文摘Some nonlinear dynamic properties of axisymmetric deformation are ex- amined for a spherical membrane composed of a transversely isotropic incompressible Rivlin-Saunders material. The membrane is subjected to periodic step loads at its inner and outer surfaces. A second-order nonlinear ordinary differential equation approximately describing radially symmetric motion of the membrane is obtained by setting the thick- ness of the spherical structure close to one. The qualitative properties of the solutions are discussed in detail. In particular, the conditions that control the nonlinear periodic oscillation of the spherical membrane are proposed. In certain cases, it is proved that the oscillating form of the spherical membrane would present a homoclinic orbit of type ＂∞＂, and the amplitude growth of the periodic oscillation is discontinuous. Numerical results are provided.
文摘The analyses of finite deformation and stress for a hyperelastic rectangular plate with some voids under an uniaxial extension were conducted. The governing differential equations were given from the incompressibility condition of the material. The solution was approximately obtained from the minimum potential energy principle. The growth of voids was discussed. One can see that an initial central circular-cylinder void becomes an elliptic-cylinder void, but an initial non-centeral circular-cylinder void becomes an elliptic-like cylinder void and the center of void has a shift. The stress distributions along the edges of voids were given and the phenomenon of stress concentration was observed. The influences of the distribution manner and size of voids, as well as the distance between them on the growth of voids were analyzed.
基金Project supported by the National Natural Science Foundation of China (No.10272069) and the Shanghai Key SubjectProgram.
文摘The e?ect of material anisotropy on the bifurcation for void formation in anisotropic compressible hyperelastic materials is examined. Numerical solutions are obtained in an anisotropic sphere, whose material is transversely isotropic in the radial direction. It is shown that the bifur- cation may occur either to the right or to the left, depending on the degree of material anisotropy. The deformation and stress contribution in the sphere before cavitation are di?erent from those after cavitation. The stability of solutions is discussed through a comparison of energy.
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.
