An anisotropic discrete fiber model with dissipation for soft biological tissues

• A model is proposed to characterize the inelastic properties of soft tissues.
• The inelastic response is characterized by only three material parameters.
• The model accurately simulated deformations of tissues with errors from 8% to 22%.

Nonlinear three-dimensional constitutive equations are developed for analyzing inelastic effects that cause dissipation in biological tissues. The model combines a structural icosahedral model of six discrete fiber bundles with a phenomenological model of the inelastic distortional deformations of the matrix containing the fibers. The inelastic response of the matrix is characterized by only three material parameters, which can be used to model both rate-independent and rate-dependent response with a smooth elastic-inelastic transition. Also, a robust, strongly objective scheme is discussed, which allows the model to be easily implemented into finite element computer codes. Examples show that the model predictions compare well with experimental data for the nonlinear, anisotropic, inelastic response of a number of tissues. Specifically, the model simulated the biaxial stretching of rabbit skin with an error of 15.7%, stress relaxation of rabbit skin with an error of 17.2%, simple shear of rat septal myocardium with an error of 21.6%, and uniaxial stress in compression of monkey liver with an error of 8.3%.