An extended lumped damage mechanics IGABEM formulation for quasi-brittle material failure

Abstract

This study proposes a new formulation for the mechanical modeling of quasi-brittle materials. The material degradation due to cracking is addressed through the Extended Lumped Damage Mechanics (XLDM) approach. The model is inserted into an IGABEM formulation, where Non-Uniform Rational B-Splines (NURBS) are the basis functions. A novel nonlinear solution technique has been developed for the numerical implementation. Crack propagation is captured using the initial stress field approach, widely utilized by the BEM community to account for nonlinear material behavior. The XLDM is coupled into an IGABEM formulation by discretizing part of the domain into cells, placed only where damage is expected to grow. Classical benchmark problems are presented to demonstrate the method’s capability and effectiveness. The results show excellent agreement with both experimental and numerical findings from the literature. Damage evolution is assessed through the band thickness opening, leading to material degradation. This method offers a new way of addressing damage mechanics problems within the BEM framework. It could benefit the BEM community, as traditional damage analysis within this numerical method often leads to significant time-consuming and elevated computational costs, which are mitigated by the formulation proposed herein.