A configurational force approach to model the branching phenomenon in dynamic brittle fracture

Abstract This publication discusses a material or configurational force approach based crack propagation scheme for dynamic fracture, in which the formulation of the material forces is derived from a Lagrangian density where inertia effects are taken into account. In dynamics, the crack driving force can generally be much larger than in the static case. In order to study the capability of the method, an algorithm based on the principle of local symmetry (PLS) is introduced into an implicit solution scheme which requires an additional iterative algorithm to seek for energy minimization. By other explicit approaches, it is not possible to study the crack bifurcation phenomenon, which is well known in dynamic fracturing. It is observed that many micro branches evolve from the main crack in case of fast crack propagation. Thus, the energy flow into the main crack tip is divided between the main crack and the micro-branches. To introduce the micro-cracking effect to the fracture toughness, a fracture criterion as a function of the crack velocity is used in the model, in order to represent realistically the resistance of the cracked structure. In conclusion, it is shown that the proposed method based on the implicit description of energy minimization, is capable of explaining the physics behind the branching phenomenon and it offers a mesh objective solution for a structure even with a coarse mesh.

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