Element-wise algorithm for modeling ductile fracture with the Rousselier yield function

Abstract

Within the theme of ductile fracture in metals, we propose an algorithm for FEM-based computational fracture based on edge rotations and smoothing of complementarity conditions. Rotation axes are the crack front nodes in surface discretizations and each rotated edge affects the position of only one or two nodes. Modified edge positions correspond to the predicted crack path. To represent softening, porous plasticity in the form of the Rousselier yield function is used. The finite strain integration algorithm makes use of a consistent updated Lagrangian formulation which makes use of polar decomposition between each increment. Constitutive updating is based on the implicit integration of a regularized non-smooth problem. The proposed alternative is advantageous when compared with enriched elements that can be significantly different than classical FEM elements and still pose challenges for ductile fracture or large amplitude sliding. For history-dependent materials, there are still some transfer of relevant quantities between meshes. However, diffusion of results is more limited than with tip or full remeshing. To illustrate the advantages of our approach, fracture examples making use of the Rousselier yield function are presented. The Ma-Sutton crack path criterion is employed. Traditional fracture benchmarks and newly proposed verification tests are solved. These were found to be very good in terms of crack path and load/displacement accuracy.