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Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations

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Abstract

Under extreme loading conditions most often the extent of material and structural fracture is pervasive in the sense that a multitude of cracks are nucleating, propagating in arbitrary directions, coalescing, and branching. Pervasive fracture is a highly nonlinear process involving complex material constitutive behavior, material softening, localization, surface generation, and ubiquitous contact. A pure Lagrangian computational method based on randomly close packed Voronoi tessellations is proposed as a rational and robust approach for simulating the pervasive fracture of materials and structures. Each Voronoi cell is formulated as a finite element using the Reproducing Kernel Method. Fracture surfaces are allowed to nucleate only at the intercell faces, and cohesive tractions are dynamically inserted. The randomly seeded Voronoi cells provide a regularized random network for representing fracture surfaces. Example problems are used to demonstrate the proposed numerical method. The primary numerical challenge for this class of problems is the demonstration of model objectivity and, in particular, the identification and demonstration of a measure of convergence for engineering quantities of interest.

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  1. Engineering Sciences Center, Sandia National Laboratories, Albuquerque, NM, 87185, USA

    Joseph E. Bishop

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  1. Joseph E. Bishop
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Correspondence to Joseph E. Bishop.

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Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.

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Bishop, J.E. Simulating the pervasive fracture of materials and structures using randomly close packed Voronoi tessellations. Comput Mech 44, 455–471 (2009). https://doi.org/10.1007/s00466-009-0383-6

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