Enhanced solid element model with embedded strong discontinuity for representation of mesoscale quasi-brittle failure

This article presents a novel two-dimensional quadrilateral solid finite element model, enhanced by incompatible modes and embedded strong discontinuity for simulation of localized failure in quasi-brittle heterogeneous multi-phase materials. The focus of interest lies in the development of discontinuities and cracks induced by both tensile and compressive loads, considering mesoscale material constituents and very complex meshes. Multiple cracks are initiated within elements using local Gauss-point criteria for crack initiation. Rankine and Maximum shear stress criteria control the crack initiation, location, and orientation depending solely on the stress state within the finite element. The model identifies distinct clusters of cracked elements and merges them into continuous cracks. A tracking algorithm ensures crack continuity, eliminating spurious cracks ahead of the crack tip to prevent crack arrest and stress locking. This approach ensures the formation of various types of cracks within the constituents of composite materials and their spontaneous coalescence forming the final failure mechanisms. The constitutive model for the crack representation is the damage softening model, which accounts for opening and sliding behavior. The efficacy of the proposed model is demonstrated through numerical simulations of heterogeneous 3-phase and 4-phase composites subjected to both tensile and compressive load cases.