A multi-phase-field method for surface tension-induced elasticity

TL;DR

This paper introduces a multi-phase-field model that couples surface energy and elasticity, accurately predicting stress distributions in complex geometries and heterogeneities, advancing understanding of surface tension effects in elastic materials.

Contribution

It presents a novel multi-phase-field framework that consistently models surface tension and elasticity coupling, validated against analytical solutions and applied to complex geometries.

Findings

Accurately reproduces stress in spherical heterogeneities.

Shows heterogeneous stress distribution in non-spherical elastic bodies.

Highlights the interplay between surface curvature and deformation.

Abstract

A consistent treatment of the coupling of surface energy and elasticity within the multi-phase- field framework is presented. The model accurately reproduces stress distribution in a number of analytically tractable, yet non-trivial, cases including different types of spherical heterogeneities and a thin plate suspending in a gas environment. It is then used to study the stress distribution inside elastic bodies with non-spherical geometries, such as a solid ellipsoid and a sintered structure. In these latter cases, it is shown that the interplay between deformation and spatially variable surface curvature leads to heterogeneous stress distribution across the specimen.