Evaluation of configurational/material forces in strain gradient elasticity theory

Abstract

Configurational mechanics enables prediction of the inhomogeneities evolution, with the added advantage of the possibility of tracking their direction of growth. It is well-established for classical elasticity but is largely unexplored for strain gradient elasticity. Until now, efforts related to strain gradient elasticity have been primarily theoretical, requiring numerical investigations. The current research is a leap forward to encompass the complexity arising due to non-intuitive higher-order gradient terms in configurational mechanics. After verifying the stability of the mixed FE solution, the concept of manufactured solutions is utilized to highlight the trustworthiness of the newly developed post-processing configurational force script. This is followed by systematic investigations of different assumptions about the Eshelby stress tensor and its corresponding outcomes. Novel results, including the cause of shielding effect of strain gradient elasticity are discussed. Current research brings in important findings from higher-order configurational mechanics, further applicable in the fracture mechanics community.