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Finite element implementation of incompressible, transversely isotropic hyperelasticity. (English) Zbl 0893.73071

Summary: This paper describes a three-dimensional constitutive model for biological soft tissues and its finite element implementation for fully incompressible material behavior. The necessary continuum mechanics background is presented, along with derivations of the stress and elasticity tensors for a transversely isotropic, hyperelastic material. A particular form of the strain energy for biological soft tissues is motivated, and a finite element implementation of this model based on a three-field variational principle (deformation, pressure and dilation) is discussed. Numerical examples are presented that demonstrate the effectiveness of this approach.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B20 Nonlinear elasticity
74L15 Biomechanical solid mechanics
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