A Microstructurally Based Orthotropic Hyperelastic Constitutive Law

Abstract

A constitutive model is developed to characterize a general class of polymer and polymer-like materials that displays hyperelastic orthotropic mechanical behavior. The strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules and the strain energy change associated with the deformation of a representative orthotropic unit cell. The ability of this model to predict nonlinear, orthotropic elastic behavior is examined by comparing the theory to experimental results in the literature. Simulations of more complicated boundary value problems are performed using the finite element method.

Constitutive modelling of passive myocardium: a structurally based framework for material characterization

“…Some of these are inappropriate for modelling myocardial tissue, including the Langevin eightchain based model of Bischoff et al (2002), which, as pointed out by Schmid et al (2008), does not reflect the morphology of the myocardium.…”

The anisotropic mechanical behaviour of electro-spun biodegradable polymer scaffolds: Experimental characterisation and constitutive formulation

“…This formulation was later extended to orthotropy (Bischoff et al, 2002a;Bischoff et al, 2002b, c) and transverse isotropy (Kuhl et al, 2005) in the context of biological soft tissues. Here, a transversely isotropic unit cell with initial cell dimensions ߦ and ߦ is considered (Kuhl et al, 2005) so that the directional reinforcement of the polymer structure is accounted for whilst also capturing the network characteristics of electro-spun fibres.…”

“…An attractive feature of these types of formulation is that, although phenomenological in nature, they can incorporate microstructural deformation mechanisms. To capture the mesh-like network characteristics of electro-spun scaffolds the 8-chain model approach first proposed by Arruda and Boyce (1993) in the context of polymer chain mechanics is followed but, borrowing from the elegant models of Bischoff et al (2002a); (2002b) and Kuhl et al (2005), modified by the introduction of two distinct characteristic dimensions of the micromechanical unit cell. However, departing from a classical entropic elasticity formulation for the stress-strain relation of polymer chains (Arruda and Boyce, 1993;Kratky and Porod, 1949), a novel formulation representing the mechanics of polymeric fibres (not polymer chains) is proposed.…”

The mechanics of soft biological composites.

“…The anisotropic viscoelastic model of [39] is an extension of the isotropic convolution integral formulation developed by [37] to include a dependence of the equilibrium stress and overstress response on the invariants of the CauchyGreen deformation and structure tensors. A more physically-based model has been developed by [8] for highly extensible soft tissues such as skin that combines the isotropic viscoelastic model of [5] for elastomers and the orthotropic hyperelastic model of [7]. The model attributes the large-deformation time-dependent behavior of the composite to the entropic and reptation mechanisms of the constituent longchain (bio)polymer molecules.…”

“…However, applying the internal variable approach to anisotropic finite-inelasticity raises important questions of how to describe the material anisotropy in the intermediate configuration. The model of [7] effectively specifies the material anisotropy in both the intermediate and reference configurations by requiring that the preferred material orientations remain the same in the two configurations. The elasto-plastic model of [73] for fabric-reinforced composites specifies the structure tensors in the reference configuration and transforms them to the intermediate configuration using the plastic part of the deformation gradient.…”