Computing forces on interface elements exerted by dislocations in an elastically anisotropic crystalline material

TL;DR

This paper introduces an analytical algorithm for calculating forces on interface elements caused by dislocations in anisotropic crystalline materials, improving accuracy and speed over traditional numerical methods.

Contribution

The authors develop a novel analytical approach using spherical harmonics to efficiently compute interface tractions in anisotropic materials, enhancing simulation capabilities.

Findings

Analytical method outperforms Gaussian quadrature in accuracy

Significantly faster computation of interface tractions

Applicable to dislocation-interface interaction simulations

Abstract

Driven by the growing interest in numerical simulations of dislocation-interface interactions in general crystalline materials with elastic anisotropy, we develop algorithms for the integration of interface tractions needed to couple dislocation dynamics with a finite element or boundary element solver. The dislocation stress fields in elastically anisotropic media are made analytically accessible through the spherical harmonics expansion of the derivative of Green's function, and analytical expressions for the forces on interface elements are derived by analytically integrating the spherical harmonics series recursively. Compared with numerical integration by Gaussian quadrature, the newly developed analytical algorithm for interface traction integration is highly beneficial in terms of both computation precision and speed.