Asymptotic analysis of hierarchical martensitic microstructure

TL;DR

This paper provides an exact energy computation and analysis of a hierarchical microstructure with a singularity in lead orthovanadate, revealing elastic behavior near the disclination point.

Contribution

It introduces a method to exactly compute energy and displacement fields in complex microstructures with singularities using linearized elasticity.

Findings

Energy cost is explicitly computed for the microstructure.

Displacement field is characterized near the singularity.

Deformation remains purely elastic close to the disclination.

Abstract

We consider a hierarchical nested microstructure, which also contains a point of singularity (disclination) at the origin, observed in lead orthovanadate. We show how to exactly compute the energy cost and associated displacement field within linearized elasticity by enforcing geometric compatibility of strains across interfaces of the three-phase mixture of distortions (variants) in the microstructure. We prove that the mechanical deformation is purely elastic and discuss the behavior of the system close to the origin.