Elastic interactions between 2D geometric defects

TL;DR

This paper presents a geometric elasticity framework to analyze interactions between 2D defects, enabling calculation of defect interaction energies in complex materials and biological systems.

Contribution

It introduces a novel geometric methodology for modeling localized stress sources as curvature defects, extending classical elasticity to nontrivial geometries.

Findings

Methodology applicable to various 2D stress sources

Calculation of interaction energies between defects

Application to amorphous materials and cell mechanics

Abstract

In this paper, we introduce a methodology applicable to a wide range of localized two-dimensional sources of stress. This methodology is based on a geometric formulation of elasticity. Localized sources of stress are viewed as singular defects---point charges of the curvature associated with a reference metric. The stress field in the presence of defects can be solved using a scalar stress function that generalizes the classical Airy stress function to the case of materials with nontrivial geometry. This approach allows the calculation of interaction energies between various types of defects. We apply our methodology to two physical systems: shear-induced failure of amorphous materials and the mechanical interaction between contracting cells.