Viscoelasticity and accretive phase-change at finite strains

TL;DR

This paper models the coupled evolution of a two-phase viscoelastic material undergoing irreversible accretion at finite strains, with applications to tumor growth and polymer gel swelling, including solution existence and interface limit analysis.

Contribution

It introduces a fully coupled model of viscoelastic phase accretion at finite strains, with proofs of solution existence and analysis of sharp-interface limits.

Findings

Solutions exist for both diffused- and sharp-interface models.

The sharp-interface limit of the model is rigorously analyzed.

The model captures the influence of mechanical state on phase growth.

Abstract

We investigate the evolution of a two-phase viscoelastic material at finite strains. The phase evolution is assumed to be irreversible: One phase accretes in time in its normal direction, at the expense of the other. Mechanical response depends on the phase. At the same time, growth is influenced by the mechanical state at the boundary of the accreting phase, making the model fully coupled. This setting is inspired by the early stage development of solid tumors, as well as by the swelling of polymer gels. We formulate the evolution problem by coupling the balance of momenta in weak form and the growth dynamics in the viscosity sense. Both a diffused- and a sharp-interface variant of the model are proved to admit solutions and the sharp-interface limit investigated.