In this paper we discuss the peridynamic analysis of dynamic crack branching in brittle materials and show results of convergence studies under uniform grid refinement (m-convergence) and under decreasing the peridynamic horizon (δ-convergence). Comparisons with experimentally obtained values are made for the crack-tip propagation speed with three different peridynamic horizons. We also analyze the influence of the particular shape of the micro-modulus function and of different materials (Duran 50 glass and soda-lime glass) on the crack propagation behavior. We show that the peridynamic solution for this problem captures all the main features, observed experimentally, of dynamic crack propagation and branching, as well as it obtains crack propagation speeds that compare well, qualitatively and quantitatively, with experimental results published in the literature. The branching patterns also correlate remarkably well with tests published in the literature that show several branching levels at higher stress levels reached when the initial notch starts propagating. We notice the strong influence reflecting stress waves from the boundaries have on the shape and structure of the crack paths in dynamic fracture. All these computational solutions are obtained by using the minimum amount of input information: density, elastic stiffness, and constant fracture energy. No special criteria for crack propagation, crack curving, or crack branching are used: dynamic crack propagation is obtained here as part of the solution. We conclude that peridynamics is a reliable formulation for modeling dynamic crack propagation.
Ha YD, Bobaru F (2009) Traction boundary conditions in peridynamics: a convergence study. Technical report Department of Engineering Mechanics, University of Nebraska–Lincoln, Lincoln, NebraskaGoogle Scholar
Ha YD, Bobaru F (2010) The effect of damage-dependent fracture energy on symmetry-breaking in dynamic brittle fracture. Technical report, Department of Engineering Mechanics, University of Nebraska–Lincoln, Lincoln, Nebraska.Google Scholar
Ha YD, Bobaru F, Parks ML (2010) Dynamic brittle fracture: crack branching predictions with peridynamics (submitted)Google Scholar
Hairer E, Lubich C, Wanner G (2003) Geometric numerical integration illustrated by the Störmer/Verlet method. Acta Numer, 1–51Google Scholar