## What is/are Isotropic Hyperelastic?

Isotropic Hyperelastic - 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.^{[1]}We present an analysis of anisotropic hyperelasticity, specifically transverse isotropy, that obtains closed-form expressions for the eigendecompositions of many common energies.

^{[2]}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.

^{[3]}The orthotropic properties of the wf-SMPC due to the woven fabric reinforcement were modeled using classical anisotropic hyperelasticity theorems.

^{[4]}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.

^{[5]}Elasticity tensors for isotropic hyperelasticity in principal stretches are formulated and implemented for the Finite Element Method.

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## 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.

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## 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.

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## 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.

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## 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.

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## 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.

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## 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.

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