On the use of finite elements with a high aspect ratio for modeling cracks in quasi-brittle materials

Abstract

A new technique for modeling cracks in quasi-brittle materials based on the use of interface solid finite elements is presented. This strategy named mesh fragmentation technique consists in introducing sets of standard low-order solid finite elements with a high aspect ratio in between regular (or bulk) elements of the mesh to fill the very thin gaps left by the mesh fragmentation procedure. The conception of this strategy is supported by the fact that, as the aspect ratio of a standard low-order solid finite element increases, the element strains also increase, approaching the same kinematics as the Continuum Strong Discontinuity Approach. As a consequence, the analyses can be performed integrally in the context of the continuum mechanics, and complex crack patterns can be simulated without the need of tracking algorithms. A tension damage constitutive relation between stresses and strains is proposed to describe crack formation and propagation. This constitutive model is integrated using an implicit-explicit integration scheme to avoid convergence drawbacks, commonly found in problems involving discontinuities. 2D and 3D numerical analyses are performed to show the applicability of the presented technique. Relevant aspects such as the influence of the thickness of the interface elements and mesh objectivity are investigated. The results show that the technique is able to predict satisfactorily the behavior of structural members involving different crack patterns, including multiple cracks, without significant mesh dependency provided that unstructured meshes are used.