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Computational Mechanics for Failure Analysis

Dr. Ted Belytschko
Department of Mechanical Engineering
Northwestern University
tedbelytschko@northwestern.edu

Abstract

Computational modeling of failure at the macroscale and nanoscale will be described. At the macroscale, two recently developed methods will be described: the extended finite element method (XFEM) and meshfree methods. The extended finite element method is a method that is able to model arbitrary growth of shear bands and cracks without remeshing. In the method, smooth interpolants, such as the standard finite element shape functions, are used for the regular part of the field and the discontinuity is added through a partition of unity. The methodology is combined with level sets so that no explicit description of the crack surface is needed: the entire description of the crack is incorporated in nodal variables on the initial mesh. The meshfree method is a method suited to more extreme failure, such as fragmentation, and it is very powerful in treating complex patterns of shear bands. Application of the method to crack growth in two and three dimensions will be presented. The presentation will conclude with some recent studies of fracture at the nanoscale by quantum and molecular mechanics methods.

Biography

Ted Belytschko's main interests are in the development of computational methods for engineering problems. Recently, he has worked on meshfree methods, techniques for representing arbitrary discontinuities in finite elements and multiscale coupling methods. He is co-author of the book Nonlinear Finite Elements for Continua and Structures with W.K. Liu and B. Moran and an editor of the International Journal for Numerical Methods in Engineering. He has received the Timoshenko Medal from the American Society of Mechanical Engineers, the Gauss-Newton Medal from the International Association for Computational Mechanics, the von Neumann Medal of the US Association for Computational Mechanics, the von Karman medal of the American Society of Civil Engineers, and several other medals and awards. He has received Honorary Doctorates from the University of Liege and the Ecole Centrale-Paris. He is a member of the U.S. National Academy of Engineering (elected in 1992) and the American Academy of Arts and Sciences (elected in 2002).