Determination of Material Parameters of EVA Foam under Uniaxial Compressive Testing Using Hyperelastic Models

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.

Isogeometric Analysis of Hyperelastic Material Characteristics for Calcified Aortic Valve

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.

A comparative study of 85 hyperelastic constitutive models for both unfilled rubber and highly filled rubber nanocomposite material

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.

CAVITATED BIFURCATION FOR INCOMPRESSIBLE HYPERELASTIC MATERIAL

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.

Continuum Constitutive Modeling for Isotropic Hyperelastic Materials

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.

Symmetry Transformations and Exact Solutions of a Generalized Hyperelastic Rod Equation

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.

Finite Element Modelling of Car Seat with Hyperelastic and Viscoelastic Foam Material Properties to Assess Vertical Vibration in Terms of Acceleration

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.

Fluid-Structure Interaction Modeling of the Living Artery: Based on the Zero-Pressure Status and the Anisotropic Hyperelastic Constitutive Model

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.

THE GROWTH OF THE VOID IN A HYPERELASTIC RECTANOULAR PLATE UNDERA UNIAXIAL EXTENSION

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.

Estimation of Isotropic Hyperelasticity Constitutive Models to Approximate the Atomistic Simulation Data for Aluminium and Tungsten Monocrystals

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.

A 3-D Visco-Hyperelastic Constitutive Model for Rubber with Damage for Finite Element Simulation

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.

Some qualitative properties of incompressible hyperelastic spherical membranes under dynamic loads

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.

Growth of Voids in a Hyperelastic Rectangular Plate

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.

CAVITATION BIFURCATION FOR COMPRESSIBLE ANISOTROPIC HYPERELASTIC MATERIALS

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.

NEW CONSTITUTIVE RELATIONSHIP OF INCOMPRESSIBLE HYPERELASTICITY

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Implementation of Particle Swarm Optimization Algorithm in Matlab Code for Hyperelastic Characterization

The purpose of this paper is to demonstrate the applicability of Particle Swarm Optimization algorithm to determine material parameters in incompressible isotropic elastic strain-energy functions using combined tension and torsion loading. Simulation of rubber behavior was conducted from the governing equations of the deformation of a cylinder composed of isotropic hyperelastic incompressible materials. Four different forms of strain-energy function were considered based respectively on polynomial, exponential and logarithmic terms to reproduce load force (N) and torque (M) trends using natural rubber experimental data. After highlighting the minimization of the objective function generated in the fitting process, the study revealed that a particle swarm optimization algorithm could be successfully used to identify the best material parameters and characterize the behavior of rubber-like hyperelastic materials.

Learning Invariant Representation of Multiscale Hyperelastic Constitutive Law from Sparse Experimental Data

Constitutive modeling of heterogeneous hyperelastic materials is still a challenge due to their complex and variable microstructures.We propose a multiscale datadriven approach with a hierarchical learning strategy for the discovery of a generic physics-constrained anisotropic constitutive model for the heterogeneous hyperelastic materials.Based on the sparse multiscale experimental data,the constitutive artificial neural networks for hyperelastic component phases containing composite interfaces are established by the particle swarm optimization algorithm.A microscopic finite element coupled constitutive artificial neural networks solver is introduced to obtain the homogenized stress-stretch relation of heterogeneous materials with different microstructures.And a dense stress-stretch relation dataset is generated by training a neural network through the FE results.Further,a generic invariant representation of strain energy function(SEF)is proposed with a parameter set being implicitly expressed by artificial neural networks(SANN),which describes the hyperelastic properties of heterogeneous materials with different microstructures.A convexity constraint is imposed on the SEF to ensure that the multiscale constitutive model is physically relevant,and the ℓ_(1) regularization combined with thresholding is introduced to the loss function of SANN to improve the interpretability of this model.Finally,the multiscale model is hierarchically trained,cross-validated and tested using the experimental data of cord-rubber composite materials with different microstructures.The proposed multiscale model provides a convenient and general methodology for constitutive modeling of heterogeneous hyperelastic materials.

Regional stretch method to measure the elastic and hyperelastic properties of soft materials

Characterizing the mechanical properties of soft materials and biological tissues is of great significance for understanding their deformation behaviors. In this paper, a regional stretching method is proposed to measure the elastic and hyperelastic properties of a soft material with an adhesive surface or with the aid of glue. Theoretical and dimensional analyses are performed to investigate the regional stretch problem for soft materials that obey the neo-Hookean model, the Mooney-Rivlin model, or the Arruda-Boyce model. Finite element simulations are made to determine the expressions of the dimensionless functions that correlate the stretch response with the constitutive parameters. Thereby, an inverse approach is established to determine the elastic and hyperelastic properties of the tested materials. The regional stretch method is also compared to the indentation technique. Finally, experiments are performed to demonstrate the effectiveness of the proposed method.

DYNAMIC CHARACTERISTICS IN INCOMPRESSIBLE HYPERELASTIC CYLINDRICAL MEMBRANES

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.

Dynamic cavitations in incompressible hyperelastic pre-strained circular sheets

A class of dynamic cavitations is examined for an isotropic incompressible hyperelastic circular sheet under a pre-strained state caused by an initially applied finite radial tension.The solutions that describe the radially symmetric motion of the pre-strained sheet are obtained.The conditions of cavitated bifurcation that describe cavity formation and motion with time at the axial line of the pre-strained sheet are proposed,that is to say,a circular cavity will form if the suddenly applied radial tensile load exceeds a certain critical value;dynamically,it is proved that the formed cavity will present a nonlinearly periodic oscillation,which is essentially different from the singular periodic oscillation of the formed cavity in an incompressible hyperelastic solid sphere.Numerical simulations show the effects of prescribed radial tension,material parameter and tensile load on critical ten-sile load describing cavity formation and periodic oscillation of the pre-strained circular sheet.