A Reactive Inelasticity Theoretical Framework for Modeling Viscoelasticity, Plastic Deformation, and Damage in Soft Tissue.

Fibrous tissues are biopolymeric materials that are made of extracellular proteins including several collagens and proteoglycans, and have a high water content. These tissues have non-linear, anisotropic, and inelastic mechanical behaviors that are often categorized into viscoelastic behavior, plastic deformation, and damage. While tissue's elastic and viscoelastic mechanical properties have been measured for decades, there is no comprehensive theoretical framework for modeling inelastic behaviors of these tissues that is based on their structure. To model the three major inelastic mechanical behaviors of tissue's fibrous matrix we formulated a structurally inspired continuum mechanics framework based on the energy of molecular bonds that break and reform in response to external loading (reactive bonds). In this framework, we employed the theory of internal state variables and kinetics of molecular bonds. The number fraction of bonds, their reference deformation gradient, and damage parameter were used as state variables that allowed for consistent modeling of all three of the inelastic behaviors of tissue by using the same sets of constitutive relations. Several numerical examples are provided that address practical problems in tissue mechanics, including the difference between plastic deformation and damage. This model can be used to identify relationships between tissue's mechanical response to external loading and its biopolymeric structure.