Viscoelasticity and accretive phase-change at finite strains

Area of Science:

• Continuum Mechanics
• Materials Science
• Biophysics

Background:

• Investigating two-phase viscoelastic materials at finite strains.
• Modeling irreversible phase evolution where one phase grows at the expense of another.
• Inspired by solid tumor development and polymer gel swelling.

Purpose of the Study:

• To develop a fully coupled model for viscoelastic material evolution with irreversible phase changes.
• To analyze the influence of mechanical state on growth dynamics at phase boundaries.
• To mathematically formulate and solve the coupled evolution problem.

Main Methods:

• Coupling the balance of momenta in weak form with growth dynamics in the viscosity sense.
• Formulating both diffused-interface and sharp-interface variants of the model.
• Investigating the sharp-interface limit of the proposed model.

Main Results:

• Proving the existence of solutions for both diffused- and sharp-interface model variants.
• Demonstrating a fully coupled system where mechanical state influences growth.
• Establishing a framework for analyzing irreversible phase evolution in viscoelasticity.

Conclusions:

• The developed model provides a robust mathematical framework for understanding irreversible phase evolution in viscoelastic materials.
• The findings are applicable to biological systems like tumor growth and engineered materials like swelling gels.
• The study confirms the solvability of both diffused and sharp interface models, paving the way for further theoretical and experimental investigations.