FINITE-ELEMENT FORMULATIONS FOR HYPERELASTIC TRANSVERSELY ISOTROPIC BIPHASIC SOFT-TISSUES

This paper presents a finite element model for the three-dimensional ( 3-D) nonlinear analysis of soft hydrated tissues such as articular car tilage in diarthrodial joints under physiologically relevant loading c onditions. A biphasic continuum description is used to represent the s oft tissue as a two-phase mixture of incompressible inviscid fluid and a hyperelastic, transversely isotropic solid. Alternate mixed-penalty and velocity-pressure finite element formulations are used to solve t he non;nonlinear biphasic governing equations, including the effects o f a strain-dependent permeability and a hyperelastic solid phase under finite deformation. The resulting first-order nonlinear system of equ ations are discretized in time using an implicit finite difference sch eme, and solved using the Newton-Raphson method. A significant contrib ution of this work is the implementation and testing of a biphasic des cription with a transversely isotropic hyperelastic solid phase. This description considers a Helmholtz free energy function of five invaria nts of the Cauchy-Green deformation tensor and the preferred direction of the material, allowing for asymmetric behavior in tension and comp ression. An exponential form is suggested, and a set of material param eters is identified to represent the response of soft tissues in range s of deformation and stress observed experimentally. After demonstrati ng the behavior of this constitutive model in simple tension and compr ession, a sample problem of unconfined compression is used to further validate the finite element implementation.