A Simplified Eulerian Formulation of a Multi-Phase Soft Tissue Model with Homeostasis and Phase Transformation

A thermomechanical large deformation Eulerian formulation of a multi-phase soft tissue model with homeostasis and phase transformation has been developed. The model has been simplified by considering a single velocity field and a single temperature field with evolution equations for volume fractions of the phases which are not driven by diffusion. Specific constitutive equations are developed for an exponential form of the Helmholtz free energy. An example of spherical expansion of a three-phase material is considered in the absence of thermal effects. This example considers phase transformations from healthy tissue to a composite of healthy, diseased and necrotic tissues. Although much work is needed to model the mechanobiological aspects of the disease progress, this simplified model indicates that the state of the tissue at the onset of its non-zero volume fraction (i.e. when it begins to influence stress) can significantly effect the resulting stress distribution.