Finite elements with embedded branching

Abstract

This paper is concerned with the numerical modeling of crack branching in brittle materials using finite elements with embedded strong discontinuities, that is, discontinuities in the displacement field defining the solution of the underlying boundary-value problem. In particular, new finite elements are developed in this framework accommodating the different branches of the bifurcating discontinuity in the element interior. The key aspect of these developments is the correct representation of the kinematics of these configurations. This is accomplished through the identification of the proper separation modes characterizing these solutions and their incorporation in the discrete strain field of the finite element. The resulting enhanced modes are activated based on a branching criterion depending on the velocity of the crack tip. The performance of the new elements is illustrated with several numerical simulations involving other approaches for the treatment of branching and comparisons with available experimental results.