Identification of cavities and inclusions in linear elasticity with a phase-field approach

TL;DR

This paper introduces a phase-field based algorithm for reconstructing cavities and inclusions in linear elastic media from boundary measurements, addressing an inverse shape problem with regularization.

Contribution

It develops a novel phase-field approach for the inverse problem of shape reconstruction in linear elasticity, incorporating perimeter regularization for robustness.

Findings

Effective reconstruction of cavities and inclusions demonstrated.

Algorithm handles small elasticity contrasts effectively.

Provides a robust computational method for inverse shape problems.

Abstract

In this paper, we deal with the inverse problem of the shape reconstruction of cavities and inclusions embedded in a linear elastic isotropic medium from boundary displacement's measurements. For, we consider a constrained minimization problem involving a boundary quadratic misfit functional with a regularization term that penalizes the perimeter of the cavity or inclusion to be identified. Then using a phase-field approach we derive a robust algorithm for the reconstruction of elastic inclusions and of cavities modeled as inclusions with a very small elasticity tensor.