Past Event: Oden Institute Seminar

The Variational Approach to Fracture for Ductile Materials

Mike Borden, Professor, Department of Civil, Construction, and Environmental Engineering, North Carolina State University

Abstract

The determination of complex three-dimensional failure processes has been difficult, if not impossible, with traditional computational approaches. Traditional finite element methods have achieved some success in two dimensions, but a satisfactory methodology for full three-dimensional configurations has never been achieved. In this presentation I will describe my work to develop a methodology for simulating three-dimensional crack propagation in both brittle and ductile materials. This methodology is based on a phase-field formulation and has several unique attributes: First, all calculations can be performed with reference to the initial mesh, and are independent of the topology of the fractured domain. Second, cracks spontaneously nucleate, bifurcate, trifurcate, etc., without any ad hoc devices determining where these events occur. Third, crack formation is not restricted or related in any way to the structure of the mesh. Fourth, the computer implementation of the formulation is remarkably simple and is exactly the same in three dimensions as it is in two dimensions. I will describe the work that is being performed in my group to apply phase-field models to dynamic fracture of brittle and ductile materials. As part of this work we have extended existing quasi-static models to dynamic fracture, and introduced a higher-order phase-field model that has shown the potential to provide higher-order accurate results for fracture. I will also discuss our current efforts to develop and quantify the constitutive theory of phase-field models for ductile fracture. Numerical results, which demonstrate that the phase-field approach is able to model complex crack behavior in both two and three dimensions, will be presented. Bio sketch: Dr. Michael Borden is an Assistant Professor in the Department of Civil, Construction, and Environmental Engineering at North Carolina State University. Mike began his academic career at Brigham Young University in Provo, Utah where he earned both a BS and MS in Civil Engineering. He then worked as a member of the technical staff at Sandia National Laboratories where he developed computational geometry methods to support Sandia’s finite element codes. After five years at Sandia, Mike went on to earn a Ph.D. in Computational Science, Engineering, and Mathematics from The University of Texas at Austin. Mike joined the faculty at NC State in 2014.