A Concurrent Multiscale Method for Nonlinear Solid Mechanics using Multigrid Concepts with Application to Metal-Additive Manufacturing

Visiting Scholar
Joe Bishop, Ph.D.
Engineering Sciences Center
Sandia National Laboratories

Friday, April 13, 3:15 pm
Sidney & Marian Green Classroom (3550 MEK)

Abstract: The predictive modeling of plasticity, damage, and fracture phenomena in polycrystalline materials is a grand challenge in solid mechanics. Two scales of primary interest are the macroscale, where engineering quantities of interest are extracted, and the mesoscale where grain-scale physics is operative. Macroscale simulations using conventional homogenized plasticity models are limited in their predictive capability, especially when the assumptions of homogenization theory, for example scale separation and statistical homogeneity, are violated. Mesoscale models of grain-scale physics simulate the plastic response of individual grains directly and are thus potentially more predictive of the overall mechanical behavior. However, the direct numerical simulation of grain-scale physics within macroscale structures is computationally prohibitive. Here, the use of geometric multigrid techniques is explored as a framework for creating a concurrent multiscale method bridging the mesoscale and macroscale for modeling the large-deformation, nonlinear, response of polycrystalline materials. Initial work and applications to materials and structures created using metal-additive manufacturing will be presented.

Bio: Joe Bishop received his Ph.D. in Aerospace Engineering from Texas A&M University in 1996. His graduate research was in the general areas of the mechanics of composite materials and material damping. From 1997 to 2004 he worked in the Synthesis & Analysis Department of the Powertrain Division of General Motors Corporation, performing thermal-structural analysis of internal combustion engines with a focus on predicting high-cycle fatigue performance of the base engine. He joined Sandia National Laboratories in 2004 in the Engineering Sciences Center. He has worked on diverse topics such as impact and penetration, pervasive-fracture modeling, geologic CO2 sequestration, polyhedral finite elements, and additive manufacturing. His current research projects include the process and performance modeling of metal-additive manufacturing, meshfree methods for modeling extreme deformation in solids, and experimental methods for determining residual-stress fields.