Multiscale Uncertainty Quantification in Solid Mechanics Using a Posteriori Error-estimation Techniques with Applications to Process-structure-performance Modeling of Laser-welded and Additively-manufactured Structures
Two fundamental sources of error and uncertainty in macroscale solid-mechanics modeling are (1) the use of an approximate material model that represents in a mean sense the complex nonlinear processes occurring at the microscale, and (2) the use of homogenization theory with implicit approximations such as a separation-of-scales and the existence of a well-defined representative volume element. Macroscopic material models are typically in error when exercised outside of the calibration regime, and the assumptions in homogenization theory are typically violated in welded regions of a structure and for additively-manufactured (AM) metallic structures. A more practical approach is a simple constitutive model is maintained at the macroscale, such as isotropic elasticity or von Mises plasticity, and the errors in engineering quantities of interest are assessed in a post-processing step using a localization process and error bounds. This approach is inherently scalable to arbitrarily large systems. Also, for a given loading scenario, the apparent macroscale properties can be adapted to minimize the goal-oriented error and uncertainty. This framework is demonstrated for laser-welded and additively-manufactured structures using a process-structure-performance modeling paradigm.
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 the mechanisms and mechanics 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 such as impact and penetration, pervasive fracture modeling, and geologic CO2 sequestration. His current research interests include multiscale modeling in support of additive manufacturing, experimental methods and computational techniques for determining residual-stress fields, polyhedral finite-element formulations and applications, and second-generation wavelets.