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Finite element formulations for hyperelastic transversely isotropic biphasic soft tissues. (English) Zbl 0920.73350
Summary: We present a finite element model for the three-dimensional nonlinear analysis of soft hydrated tissues such as articular cartilage in diarthrodial joints under physiologically relevant loading conditions. A biphasic continuum description is used to represent the soft tissue as a two-phase mixture of incompressible inviscid fluid and a hyperelastic, transversely isotropic solid. Then alternate mixed-penalty and velocity-pressure finite element formulations are used to solve the nonlinear biphasic governing equations, including the effects of a strain-dependent permeability and a hyperelastic solid phase under finite deformation. The resulting first-order nonlinear system of equations are discretized in time using an implicit finite difference scheme, and solved using the Newton-Raphson method. We also implement and test a biphasic model with a transversely isotropic hyperelastic solid phase. This model considers a Helmholtz free energy function of five invariants of the Cauchy-Green deformation tensor and the preferred direction of the material, allowing for asymmetric behavior in tension and compression. An exponential form is suggested, and a set of material parameters is identified to represent the response of soft tissues in ranges of deformation and stress observed experimentally. After demonstrating the behavior of this constitutive model in simple tension and compression, a sample problem of unconfined compression is used to further validate the finite element implementation.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74L15 Biomechanical solid mechanics
92C10 Biomechanics
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