## What is/are Isotropic Hyperelastic?

Isotropic Hyperelastic - The paper deals with the finite bending analysis of transversely isotropic hyperelastic slender beams made of a neo-Hookean material with longitudinal voids.^{[1]}Design examples involving three objective functions are presented, demonstrating the efficiency and effectiveness of the proposed framework in designing anisotropic hyperelastic structures under large deformations.

^{[2]}The present paper proposes a new Strain Energy Function (SEF) for incompressible transversely isotropic hyperelastic materials, i.

^{[3]}Such a formulation is valid for general three-dimensional geometries and isotropic hyperelastic materials.

^{[4]}In this work, a phenomenological approach is used to construct a model of the effective material, where the inhomogeneous rubber-cord layer is replaced by an equivalent homogeneous anisotropic hyperelastic material.

^{[5]}Furthermore, this study reviewed various forms of passive constitutive models for the highly fibrous colorectal tissue ranging from the simplest linearly elastic and the conventional isotropic hyperelastic to the most sophisticated second harmonic generation image based anisotropic mathematical formulation.

^{[6]}While the native menisci were modeled using the nonlinear hyperelastic Holzapfel-Gasser-Ogden (HGO) constitutive model, the meniscal implant was modeled using the isotropic hyperelastic neo-Hookean model.

^{[7]}Herein, the PV was assumed to behave like an anisotropic hyperelastic material with circumferentially-aligned fibers.

^{[8]}This research presents the adaptation of an anisotropic hyperelastic constitutive model for predicting the experimentally observed in-plane, orthotropic, bi-modular and nonlinear-elastic responses.

^{[9]}The biological tissue and the silicone were modeled with a fiber-oriented anisotropic and isotropic hyperelastic model, respectively.

^{[10]}Simulation of rubber behavior was conducted from the governing equations of the deformation of a cylinder composed of isotropic hyperelastic incompressible materials.

^{[11]}In this work, the equilibrium problem of anisotropic hyperelastic graphene membranes is addressed.

^{[12]}Various options and features of the proposed anisotropic hyperelastic model are investigated.

^{[13]}Isotropic hyperelastic relations between stresses and elastic strains are assumed.

^{[14]}The strain-energy density W $W$ for incompressible transversely isotropic hyperelastic materials depends on four independent invariants of the strain tensor.

^{[15]}The objective of the current study is to use the Small On Large (SOL) theory to linearize the anisotropic hyperelastic behavior in order to propose a reduced-order model for FSI simulations of the aorta.

^{[16]}We further demonstrate that for a nonlinear cardiac mechanics model, using our reconstructed LV geometries instead of manually extracted ones only moderately affects the inference of passive myocardial stiffness described by an anisotropic hyperelastic constitutive law.

^{[17]}Mechanical tests were conducted to estimate the stress-stretch responses, which were compared with natural skin properties, and further characterized using isotropic and anisotropic hyperelastic formulations.

^{[18]}The present work contributes towards a comprehensive DJ-TLED algorithm concerning isotropic and anisotropic hyperelastic constitutive models and GPU implementation.

^{[19]}In FE simulation, the dermis and subcutaneous tissue were modeled as anisotropic hyperelastic material and isotropic elastic material, respectively.

^{[20]}This analysis was completed in providing a range of isotropic hyperelastic coefficients to take into account the toe region.

^{[21]}For finite-strain plasticity with anisotropic yield functions and anisotropic hyperelasticity, we use the Kroner-Lee decomposition of the deformation gradient combined with a yield function written in terms of the Mandel stress.

^{[22]}To investigate the effect of probabilistic parameters on predicted mechanical responses, we study radial oscillations of cylindrical and spherical shells of stochastic incompressible isotropic hyperelastic material, formulated as quasi-equilibrated motions where the system is in equilibrium at every time instant.

^{[23]}Mechanical properties of PV leaflet were obtained from biaxial testing of human PV leaflet, and characterized by an anisotropic hyperelastic material model.

^{[24]}Two anisotropic hyperelastic material models were investigated and implemented in Abaqus as a user-defined material.

^{[25]}Aiming at simplicity, we analyze a model of bilayered isotropic hyperelastic (neo-Hookean) spherical shells with residual stresses generated by "shrink-fitting" two perfectly bonded layers with radial interfacial incompatibility.

^{[26]}For anisotropic hyperelastic tubes where the material parameters are single-valued constants, the problem has been satisfactorily addressed.

^{[27]}One of the most used models is the eight chain model, being its salient feature that it reproduces the overall response of isotropic hyperelastic materials with only two material parameters obtained from a tensile test.

^{[28]}In this study we propose, for each of the tissues involved, a new formulation of the so-called transversely isotropic hyperelastic model (TIHM).

^{[29]}The numerical scheme is also examined under compressive and tensile loads for isotropic and anisotropic hyperelastic materials.

^{[30]}In this paper, a nonlinear anisotropic hyperelastic constitutive model is proposed to consider this tension–shear coupling effect.

^{[31]}A nonlinear anisotropic hyperelastic constitutive model is developed for plain weave fabrics by considering biaxial tensile coupling.

^{[32]}We present an analysis of anisotropic hyperelasticity, specifically transverse isotropy, that obtains closed-form expressions for the eigendecompositions of many common energies.

^{[33]}A new anisotropic hyperelastic model has been developed to model the deformation response of a knitted-fabric-reinforced rubber composite.

^{[34]}This work presents a novel frequency-domain Green function method to describe and model nonlinear wave interactions in isotropic hyperelastic media.

^{[35]}The non-affine equal-force model is compared to the common affine model and a hybrid equal-force model from the literature, when considering the isotropic hyperelastic behavior without damage of rubber materials presenting chains of various lengths.

^{[36]}In this work, we developed the displacement-based computationally efficient volumetric locking-free 3D finite element using smoothening of determinant of deformation gradient (J-Bar method) within the framework of isotropic hyperelasticity.

^{[37]}The orthotropic properties of the wf-SMPC due to the woven fabric reinforcement were modeled using classical anisotropic hyperelasticity theorems.

^{[38]}First, the normal stresses of the inner reticulated fabric rubber composite are determined based on the anisotropic hyperelastic constitutive model and the corresponding hyperelastic material parameters under different temperatures are obtained using the normal stress equations to fit the experimental results.

^{[39]}An anisotropic hyperelastic model based on strain energy decomposition is proposed.

^{[40]}We demonstrate our method in a finite deformation setting of an initially isotropic hyperelastic material of Ogden class which is often modeling biological tissue.

^{[41]}In the present study, a compressible anisotropic hyperelastic strain energy density function (SEDF) is developed to capture the in-plane nonlinear elastic responses of a commercial Fiberglass/Phenolic hexagonal cell honeycomb core under large deformations.

^{[42]}We describe a non-linear anisotropic hyperelastic model appropriate for geomaterials, deriving the full stress-strain response from strain energy or complementary energy functions.

^{[43]}This study investigates axisymmetric fractional vibration of an isotropic hyperelastic semi-linear thin disc with a view to examine effects of finite deformation associated with the material of the disc and effects of fractional vibration associated with the motion of the disc.

^{[44]}Two representative examples are studied: the compression of an isotropic hyperelastic cube and the tensile test of a fully-incompressible anisotropic hyperelastic arterial wall model.

^{[45]}The continuum formulation uses an anisotropic hyperelastic material model in the framework of the geometrically exact Kirchhoff-Love shell theory and isogeometric finite elements.

^{[46]}A new anisotropic finite strain viscoelastic model is presented, which is based on the Holzapfel type anisotropic hyperelastic strain-energy function.

^{[47]}The model in this work is based on the anisotropic hyperelasticity assumption (the transversely isotropic case) together with modelling of the evolving load-carrying capacity (scalar damage) whose change is governed by the Caputo-Almeida fractional derivative.

^{[48]}An anisotropic hyperelastic model (Gasser-Ogden-Holzapfel) was used to model the quasi-static behaviour of the tissue, whereas three different isotropic hyperelastic models (Fung, Gent and Ogden) were used to model the behaviour of scalp tissue at higher strain rates.

^{[49]}Elasticity tensors for isotropic hyperelasticity in principal stretches are formulated and implemented for the Finite Element Method.

^{[50]}

## Transversely Isotropic Hyperelastic

The paper deals with the finite bending analysis of transversely isotropic hyperelastic slender beams made of a neo-Hookean material with longitudinal voids.^{[1]}The present paper proposes a new Strain Energy Function (SEF) for incompressible transversely isotropic hyperelastic materials, i.

^{[2]}The strain-energy density W $W$ for incompressible transversely isotropic hyperelastic materials depends on four independent invariants of the strain tensor.

^{[3]}In this study we propose, for each of the tissues involved, a new formulation of the so-called transversely isotropic hyperelastic model (TIHM).

^{[4]}The results obtained in three inverse problems regarding composite and transversely isotropic hyperelastic materials/structures with up to 17 unknown properties clearly demonstrate the validity of the proposed approach, which allows to significantly reduce the number of structural analyses with respect to previous SA/HS/BBBC formulations and improves robustness of metaheuristic search engines.

^{[5]}

## isotropic hyperelastic material

The present paper proposes a new Strain Energy Function (SEF) for incompressible transversely isotropic hyperelastic materials, i.^{[1]}Such a formulation is valid for general three-dimensional geometries and isotropic hyperelastic materials.

^{[2]}In this work, a phenomenological approach is used to construct a model of the effective material, where the inhomogeneous rubber-cord layer is replaced by an equivalent homogeneous anisotropic hyperelastic material.

^{[3]}Herein, the PV was assumed to behave like an anisotropic hyperelastic material with circumferentially-aligned fibers.

^{[4]}The strain-energy density W $W$ for incompressible transversely isotropic hyperelastic materials depends on four independent invariants of the strain tensor.

^{[5]}In FE simulation, the dermis and subcutaneous tissue were modeled as anisotropic hyperelastic material and isotropic elastic material, respectively.

^{[6]}To investigate the effect of probabilistic parameters on predicted mechanical responses, we study radial oscillations of cylindrical and spherical shells of stochastic incompressible isotropic hyperelastic material, formulated as quasi-equilibrated motions where the system is in equilibrium at every time instant.

^{[7]}Mechanical properties of PV leaflet were obtained from biaxial testing of human PV leaflet, and characterized by an anisotropic hyperelastic material model.

^{[8]}Two anisotropic hyperelastic material models were investigated and implemented in Abaqus as a user-defined material.

^{[9]}One of the most used models is the eight chain model, being its salient feature that it reproduces the overall response of isotropic hyperelastic materials with only two material parameters obtained from a tensile test.

^{[10]}The numerical scheme is also examined under compressive and tensile loads for isotropic and anisotropic hyperelastic materials.

^{[11]}We demonstrate our method in a finite deformation setting of an initially isotropic hyperelastic material of Ogden class which is often modeling biological tissue.

^{[12]}The continuum formulation uses an anisotropic hyperelastic material model in the framework of the geometrically exact Kirchhoff-Love shell theory and isogeometric finite elements.

^{[13]}The results obtained in three inverse problems regarding composite and transversely isotropic hyperelastic materials/structures with up to 17 unknown properties clearly demonstrate the validity of the proposed approach, which allows to significantly reduce the number of structural analyses with respect to previous SA/HS/BBBC formulations and improves robustness of metaheuristic search engines.

^{[14]}

## isotropic hyperelastic model

The biological tissue and the silicone were modeled with a fiber-oriented anisotropic and isotropic hyperelastic model, respectively.^{[1]}Various options and features of the proposed anisotropic hyperelastic model are investigated.

^{[2]}In this study we propose, for each of the tissues involved, a new formulation of the so-called transversely isotropic hyperelastic model (TIHM).

^{[3]}A new anisotropic hyperelastic model has been developed to model the deformation response of a knitted-fabric-reinforced rubber composite.

^{[4]}An anisotropic hyperelastic model based on strain energy decomposition is proposed.

^{[5]}We describe a non-linear anisotropic hyperelastic model appropriate for geomaterials, deriving the full stress-strain response from strain energy or complementary energy functions.

^{[6]}An anisotropic hyperelastic model (Gasser-Ogden-Holzapfel) was used to model the quasi-static behaviour of the tissue, whereas three different isotropic hyperelastic models (Fung, Gent and Ogden) were used to model the behaviour of scalp tissue at higher strain rates.

^{[7]}

## isotropic hyperelastic constitutive

This research presents the adaptation of an anisotropic hyperelastic constitutive model for predicting the experimentally observed in-plane, orthotropic, bi-modular and nonlinear-elastic responses.^{[1]}We further demonstrate that for a nonlinear cardiac mechanics model, using our reconstructed LV geometries instead of manually extracted ones only moderately affects the inference of passive myocardial stiffness described by an anisotropic hyperelastic constitutive law.

^{[2]}The present work contributes towards a comprehensive DJ-TLED algorithm concerning isotropic and anisotropic hyperelastic constitutive models and GPU implementation.

^{[3]}In this paper, a nonlinear anisotropic hyperelastic constitutive model is proposed to consider this tension–shear coupling effect.

^{[4]}A nonlinear anisotropic hyperelastic constitutive model is developed for plain weave fabrics by considering biaxial tensile coupling.

^{[5]}First, the normal stresses of the inner reticulated fabric rubber composite are determined based on the anisotropic hyperelastic constitutive model and the corresponding hyperelastic material parameters under different temperatures are obtained using the normal stress equations to fit the experimental results.

^{[6]}

## isotropic hyperelastic behavior

The objective of the current study is to use the Small On Large (SOL) theory to linearize the anisotropic hyperelastic behavior in order to propose a reduced-order model for FSI simulations of the aorta.^{[1]}The non-affine equal-force model is compared to the common affine model and a hybrid equal-force model from the literature, when considering the isotropic hyperelastic behavior without damage of rubber materials presenting chains of various lengths.

^{[2]}

## isotropic hyperelastic strain

In the present study, a compressible anisotropic hyperelastic strain energy density function (SEDF) is developed to capture the in-plane nonlinear elastic responses of a commercial Fiberglass/Phenolic hexagonal cell honeycomb core under large deformations.^{[1]}A new anisotropic finite strain viscoelastic model is presented, which is based on the Holzapfel type anisotropic hyperelastic strain-energy function.

^{[2]}