Past Event: Oden Institute Seminar

Multiscale analysis in solids with unseparated scales: fine-scale recovery, error estimation, and coarse-scale adaptivity

Joseph Bishop, Principal Member, Technical Staff, Sandia National Laboratories

Abstract

Modeling the macroscale response of a structure requires the use of a material constitutive model that provides  the effective or homogenized behavior of the underlying material microstructure.  Assuming that homogenized properties exist for the given microstructure, there is also an inherent assumption of a separation of scales when the properties are used to predict the macroscale response of a structure.  There are several engineering applications in which these assumptions may be violated, in particular for metallic structures obtained through additive manufacturing.  Instead of resorting to direct numerical simulation of the macroscale system with an embedded fine scale, an alternative approach is to use an approximate macroscale constitutive model, but then estimate the model-form error using a posteriori estimation techniques and subsequently adapt the macroscale model to reduce the error for a given boundary value problem and quantity of interest.  We investigate this approach to multiscale analysis in solids with unseparated scales using the example of an additively-manufactured metallic structure consisting of a polycrystalline microstructure that is neither periodic nor statistically homogeneous.  As a first step to the general nonlinear case, we focus here on linear elasticity in which each grain within the polycrystal is linear elastic but anisotropic.

Biography

Joe Bishop received his Ph.D. in Aerospace Engineering from Texas A&M University in 1996.  His graduate research was in the mechanics of composite materials and mechanisms of 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 including pervasive-fracture, impact and penetration, geologic CO2 sequestration, metal additive manufacturing, residual stress measurement techniques, polyhedral finite element formulations, meshfree methods, and multiscale simulations in solid mechanics.  He is currently the manager of a modeling and simulation department within the Engineering Sciences Center at Sandia.