A mesh-size-objective modeling of quasi-brittle material using micro-cell informed damage law

A multi-scale approach for mesh size independent finite element analysis of quasi-brittle material is proposed in this article. The homogenization based multi-scale damage representation is first introduced in obtaining the damage law from micro-cell simulation with consideration of microscopic crack propagation. The key idea to remedy the mesh size sensitivity in the 2D macroscopic finite element analysis is to introduce a damage law directly from the micro-cell simulation, where the micro-cell size should be identical to the macroscopic mesh size. The micro-cells with different sizes are generated and the corresponding simulations are presented in the numerical tests to obtain the micro-cell dependent damage law. The mesh independent finite element analysis results of the notched beam and the double-edge notched specimen affirm the strategy of correcting the mesh sensitivity.