Download or read book The Variational Approach to Brittle Fracture in Materials with Anisotropic Surface Energy and in Thin Sheets written by Bin Li and published by . This book was released on 2016 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fracture mechanics of brittle materials has focused on bulk materials with isotropic surface energy. In this situation different physical principles for crack path selection are very similar or even equivalent. The situation is radically different when considering crack propagation in brittle materials with anisotropic surface energy. Such materials are important in applications involving single crystals, extruded polymers, or geological and organic materials. When this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. Thus, this situation interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Similarly, tearing of brittle thin elastic sheets, ubiquitous in nature, technology and daily life, challenges our understanding of fracture. Since tearing typically involves large geometric nonlinearity, it is not clear whether the stress intensity factors are meaningful or if and how they determine crack propagation. Geometry, together with the interplay between stretching and bending deformation, leads to complex behaviors, restricting analytical approximate solutions to very simplified settings and specific parameter regimes. In both situations, a rich and nontrivial experimental record has been successfully understood in terms of simple energetic models. However, general modeling approaches to either fracture in the presence of strong surface energy anisotropy or to tearing, capable of exploring new physics, have been lacking. The success of energetic simple models suggests that variational theories of brittle fracture may provide a unifying and general framework capable of dealing with the more general situations considered here. To address fracture in materials with strongly anisotropic surface energy, we propose a variational phase-field model resorting to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture, and reproduce strikingly well recent experimental observations. To explore tearing of thin films, we develop a geometrically exact model and a computational framework coupling elasticity (stretching and bending), fracture, and adhesion to a substrate. We numerically implement the model with subdivision surface finite elements. Our simulations qualitatively and quantitatively reproduced the crack patterns observed in tearing experiments. Finally, we examine how shell geometry affects fracture. As suggested by previous results and our own phase-field simulations, shell shape dramatically affects crack evolution and the effective toughness of the shell structure. To gain insight and eventually develop new concepts for optimizing the design of thin shell structures, we derive the configurational force conjugate to crack extension for Koiter's linear thin shell theory. We identify the conservative contribution to this force through an Eshelby tensor, as well as non-conservative contributions arising from curvature.