Comparison of local, gradient-enhanced and integral form of continuum damage approaches to strain localization in fiber reinforced composites

Structures often have inserts and notches that cause stress concentration and consequent reduction in the load bearing capacity. The literature on numerical implementation of continuum damage mechanics (CDM) has generally focused on using local theories of damage. However, their use to analyze deformations of notched laminates that are prone to strain localization can cause numerical convergence issues that can be alleviated by employing a non-local theory. There are a few studies using a non-local damage theory for fiber-reinforced polymeric composites (FRPCs) and even fewer for strain localization in FRPCs. The non-local theories employ an equivalent (or effective or von Mises) strain often used in metal plasticity while most theories for studying failure of FRPCs use individual strain/stress components. Here, we compare predictions from local and nonlocal CDM approaches that are effective in studying strain localization in FRPCs. For the local approach, we employ a rate-dependent evolution relation. For the non-local approach, we either compute damage at a point as the weighted sum of damage at its neighbors that introduces a length scale into the problem, or employ a gradient-enhanced approach that also introduces a length scale. It is shown that numerical predictions from both the rate-dependent and the non-local theory alleviate to different degrees sensitivity of results to the finite element mesh used and the strain localization issues. Of these, a local rate-type approach is more convenient and cost effective.