Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions

Schröder, Jörg; Neff, Patrizio

doi:10.1016/s0020-7683(02)00458-4

Cited by 364 publications

(277 citation statements)

References 30 publications

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“…Several different models of this type have been investigated and found to provide reasonably accurate predictions of cartilage in confined compression, unconfined compression, and tension (Klisch 2006a). The current model is a simplified version of those studied previously with the collagen modeled as a compressible Neo-Hookean material (Schroder and Neff 2003) (see Appendix B for more details on bimodular materials). For example, the SM stress equation that describes the constitutive behavior of the specimen as growth …”

Section: Materials Characterization and Parametersmentioning

confidence: 99%

A nonlinear finite element model of cartilage growth

Davol

Bingham

Sah

et al. 2007

Biomech Model Mechanobiol

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The long range objective of this work is to develop a cartilage growth finite element model (CGFEM), based on the theories of growing mixtures that has the capability to depict the evolution of the anisotropic and inhomogeneous mechanical properties, residual stresses, and nonhomogeneities that are attained by native adult cartilage. The CGFEM developed here simulates isotropic in vitro growth of cartilage with and without mechanical stimulation. To accomplish this analysis a commercial finite element code (ABAQUS) is combined with an external program (MAT-LAB) to solve an incremental equilibrium boundary value problem representing one increment of growth. This procedure is repeated for as many increments as needed to simulate the desired growth protocol. A case study is presented utilizing a growth law dependent on the magnitude of the diffusive fluid velocity to simulate an in vitro dynamic confined compression loading protocol run for 2 weeks. The results include changes in tissue size and shape, nonhomogeneities that develop in the tissue, as well as the variation that occurs in the tissue constitutive behavior from growth.

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Section: Materials Characterization and Parametersmentioning

confidence: 99%

A nonlinear finite element model of cartilage growth

Davol

Bingham

Sah

et al. 2007

Biomech Model Mechanobiol

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“…While the invariants tr(CL i ), i = 0, 1, ..., n, and trC 3 are convex with respect to F, the terms tr(C 2 L i ), i = 1, 2, ..., n, are not. However, they can be expressed in terms of convex invariants with respect to F, adjF and detF [1,5] which leads to the alternative representation of the strain energy…”

Section: Materials Symmetrymentioning

confidence: 99%

A generalized polyconvex hyperelastic model for anisotropic solids

Ehret

Itskov

2006

Proc Appl Math and Mech

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A generalized polyconvex hyperelastic model for anisotropic solids is presented. The strain energy function is formulated in terms of convex functions of generalized invariants and is given by a series with an arbitrary number of terms. The model addresses solids with orthotropic or transversely isotropic material symmetry as well as fiber-reinforced materials. Special cases of the strain energy function suitable for anisotropic elastomers and soft biological tissues are proposed.

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“…In case of isotropy there already exist some polyconvex models; the first transversely isotropic and orthotropic energies satisfying the polyconvexity condition are proposed in [7,8]. A direct extension of [8] to materials with cubic symmetry is given in [6].…”

Section: Introductionmentioning

confidence: 99%

Polyconvex Models for Arbitrary Anisotropic Materials

Ebbing

Schröder

Neff

2008

Proc Appl Math and Mech

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In this work we provide polyconvex models for arbitrary anisotropic materials. The fundamental idea is the introduction of second-order, symmetric and positive definite structural tensors which are motivated by some basic crystallographic geometric relations. The deduced invariant functions automatically satisfy the polyconvexity condition and ensure the requirement of a stress free reference configuration. Restrictions coming along with the polyconvexity condition and the usage of second-order structural tensors will be pointed out. Furthermore the results of three representative fittings show the adaptability of the proposed models for the description of real anisotropic material behavior.

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Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions

Cited by 364 publications

References 30 publications

A nonlinear finite element model of cartilage growth

A nonlinear finite element model of cartilage growth

A generalized polyconvex hyperelastic model for anisotropic solids

Polyconvex Models for Arbitrary Anisotropic Materials

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