Efficient Energy Release Rate Computations for Cracks with Arbitrary Location and Geometry

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

The goal of this fracture mechanics project is to utilize the topological derivative to approximate the energy release rate (ERR) field associated with a (small) crack of arbitrary parameterized geometry. The proposed method is radically different from, and substantially more efficient than, conventional finite element method (FEM), generalized FEM and extended FEM treatment of fracture problems. Indeed, it eliminates the need to discretize the cracked structural component. Rather it provides an approximation of the ERR for a crack of arbitrary geometry located anywhere in the solid by simply evaluate the stress field present in the loaded un-cracked component. This analysis needs to be conducted only once and with a finite element mesh substantially coarser than that needed to model the cracked specimen (since there is no need to capture the stress concentration at a crack front). Moreover it uses conventional FEA methods and thereby it eliminates the need for specialty elements. Ultimately it will be used to generate finite element contour plots that illustrate critical crack geometries throughout the body. Whence, potential failure locations and critical inspection sites can be readily identified. In this proposal, the preliminary results that are limited to 2-D homogenous isotropic linear elastic structures will be extended to heterogeneous, anisotropic, nonlinear three-dimensional structures. Moreover, the first-order approximation will be extended to achieve second-order accuracy. The successful completion of this project will lead to a novel computational design tool that is substantially more efficient than conventional. By substantially facilitating the fracture-based analysis of structural components, the method is expected to have a major impact in all industries for which the design of structural components is dictated by the presence of critical flaws. The method will also be incorporated in the graduate course on fracture mechanics that attracts students from across the College of Engineering. Through the office of Engineering On-Line Education at the University of Illinois, this course will be made available outside the University, and especially to Minority Serving Institutions (MSI).