Variational Constituive Models for Soft Biological Tissues

Biological soft tissues are heterogeneous composite materials made of cells and molecules of the extracellular matrix. These tissues are frequently classified into four basic categories: muscle, epithelial, nervous and connective, each one with its own mechanical and functional properties. Their mechanical response to external forces (excluding those mechanisms associated with time scales typical of tissue remodeling), are characterized by anisotropy, high nonlinearity, strain rate dependency, permanent deformation and eventually, damage. Despite a wide set of constitutive models that have already been proposed in the specialized literature to represent the macroscopic behavior of these materials, this work focuses attention on a particular group, coined as variational in the sense that the incremental internal variable updates are found as minimizers of a pseudo strain-energy potential, called Incremental Potential evaluated at each time-step. General cases of models for viscoelastic, viscoplastic and fiber reinforced soft materials are discussed with the aid of numerical examples exploring the features of the corresponding approach.