One-dimensional study of boundary effects and damage diffusion for regularized damage models

Abstract

Local Continuum Damage Mechanics models cannot represent the entire degradation process in materials exhibiting strain-softening behaviors. It is well known that the rate equilibrium problem becomes ill-posed when softening occurs, and an infinity of solutions exists. From a numerical point of view, finite element analyses suffer from mesh-dependent results. Non-local models are generally used to regularize the structural response and recover objectivity. However, some physical inconsistencies can be observed in numerical results, e.g., damage diffusion over large damaged bands and damage attraction on the boundary of the computational domain. Non-local formulations with evolving interactions may better describe the damaging process and overcome these issues. This paper uses the so-called spalling test to underline the main drawbacks and advantages of several regularized models with constant and evolving non-local interactions. Concerning non-local formulations with constant interactions, attention is focused on the integral non-local formulation on the internal variable of the constitutive model and an implicit gradient damage formulation. Regarding formulations with evolving non-local interactions, attention is focused on a “stress-based integral non-local” approach and the so-called “eikonal non-local” approach. In this latter case, both its integral-type and gradient-type variants are considered.

Keywords

• Damage diffusion
• Damage
• Non-local regularization
• Spalling test
• Boundary effects
• Damage diffusion