Solid phase transitions in the liquid limit

TL;DR

This paper investigates the fundamental differences between solid-solid and liquid-liquid phase transitions using a 2D nonlinear elasticity model, providing bounds on the elastic binodal near the liquid limit without explicit quasiconvex envelope computation.

Contribution

It introduces a novel approach to compare nucleation thresholds in a two-phase material to bound phase transition boundaries near the liquid limit.

Findings

Derived tight bounds on the elastic binodal for the model material.

Compared cooperative and non-cooperative nucleation to understand phase transition limits.

Provided insights into the nature of solid-solid transitions in a near-liquid regime.

Abstract

We address the fundamental difference between solid-solid and liquid-liquid phase transitions within the Ericksen's nonlinear elasticity paradigm. To highlight ideas, we consider the simplest nontrivial 2D problem and work with a prototypical two-phase Hadamard material which allows one to weaken the rigidity and explore the nature of solid-solid phase transitions in a ``near-liquid'' limit. In the language of calculus of variations we probe limits of quasiconvexity in an ``almost liquid'' solid by comparing the thresholds for cooperative (laminate based) and non-cooperative (inclusion based) nucleation. Using these two types of nucleation tests we obtain for our model material surprisingly tight two-sided bounds on the elastic binodal without directly computing the quasiconvex envelope.