Past Event: Oden Institute Seminar

Part 1: A finite-element formulation for general polyhedra in nonlinear solid mechanics. Part 2: Understanding material variability and the accuracy of homogenization in polycrystalline materials through direct numerical simulations

Joseph E. Bishop, Computational Structural Mechanics and Applications, Sandia National Laboratories

Abstract

Part 1: A displacement-based finite-element formulation for general polyhedra using harmonic shape functions is presented for applications in nonlinear solid mechanics. The two main motivations for developing polyhedral finite elements are (1) increased flexibility in discretizing geometrically complex structures, both engineered and natural, and (2) the modeling of pervasive-fracture processes using random close-packed Voronoi meshes. Part 2: In order to understand how microscale material variability is manifested at the macroscale, an ensemble of direct numerical simulations (DNS) is performed. Each simulation models a random polycrystalline microstructure embedded directly in a macroscale structure. These DNS results are compared to simulations based on the governing equations and material properties obtained from first-order homogenization theory. Quantitative comparisons are made in both the elastic and elastic-plastic regimes. Bio Joe Bishop received his Ph.D. in Aerospace Engineering from Texas A&M University in 1996. His graduate research was in the general area of composite materials and fracture mechanics. 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. He joined Sandia National Laboratories in 2004 in the Computational Solid Mechanics group. His research interests include pervasive-fracture modeling, computational homogenization and multi-scale analysis, error estimation in finite-element simulations, and computational approaches for enabling a rapid design-to-analysis paradigm.