Theory and finite element implementation of orthotropic and transversely isotropic incompressible hyperelastic membrane

Purpose - The purpose of this paper is to describe a general theoretical and finite element implementation framework for the constitutive modelling of biological soft tissues. Design/methodology/approach - The model is based on continuum fibers reinforced composites in finite strains. As an extension of the isotropic hyperelasticity, it is assumed that the strain energy function is decomposed into a fully isotropic component and an anisotropic component. Closed form expressions of the stress tensor and elasticity tensor are first established in the general case of fully incompressible plane stress which orthotropic and transversely isotropic hyperelasticity. The incompressibility is satisfied exactly. Findings - Numerical examples are presented to illustrate the model's performance. Originality/value - The paper presents a constitutive model for incompressible plane stress transversely isotropic and orthotropic hyperelastic materials.