Studies on Strain Softening Materials using Nonlocal Finite Element and Element-Free Galerkin Methods

Abstract

The present work simulates the failure phenomenon of various materials in nonlocal finite element (FEM) and element-free Galerkin (EFG) methods. It commences by examining the constraints inherent in conventional FEM, especially in its application to adhesive bonded joints. Subsequently, it introduces the nonlocal integral theories to accurately capture numerically converged structural responses in complex mode-I and mixed-mode problems within a thermodynamic framework, selecting strain as the regularized variable. Building on the limitations of the nonlocal strain approach, including its tendency to underestimate peak loads and high computational time, the study proposes a strain difference-based method to enhance the prediction of failure behaviour and damage/crack propagation in quasi-brittle materials within a thermodynamic framework. The study then delves into ductile materials exploring the concepts of continuum damage mechanics (CDM) to propose a new nonlocal equivalent plastic strain based ductile damage model which is relatively simpler, reduces the number of material parameters, and enhances the understanding of ductile damage behaviour. A nonlocal equivalent plastic strain is integrated with the proposed damage model to address the challenges associated with strain localization.