| Accurate computational models of joint mechanics require robust numerical representations of biological materials such as ligaments, tendon, and cartilage. This thesis describes the development of a three-dimensional constitutive model to represent ligaments and tendons and a finite element implementation of this model for fully incompressible material behavior. The necessary continuum mechanics background is presented, with emphasis on the form of the stress and elasticity tensors for a transversely isotropic hyperelastic material. Restrictions are derived for the strain energy to ensure that the equilibrium equations remain elliptic. In situ experimental testing of tendons was performed to assess the ability of the constitutive model to describe and predict material behavior. For the finite element implementation, a multiplicative split of the deformation gradient into deviatoric and dilational parts is employed. This provides the framework for an uncoupled strain energy function and leads to a three-field variational principle in which the deformation, pressure, and volume ratio (dilation) are field variables. By eliminating the dilation and pressure at the element level, an efficient generalized displacement finite element treatment is obtained, with the capability to handle incompressible behavior without "locking." Numerical examples are presented that demonstrate the utility and effectiveness of this approach for incompressible, transversely isotropic soft tissues including ligaments and tendons. |
