Mechanical and Civil Engineering Seminar

Mechanical and Civil Engineering Seminar Series

Title: Accelerated Computing of Deformation and Failure in Porous Materials

Abstract: The deformation and failure of porous materials is of primary interest in a range of applications, from the design of lightweight high-strength materials for aircraft wings, shock absorbers in military vehicles, and construction of civilian infrastructure, to the high-precision engineering of the subsurface for geothermal energy extraction by hydrofracking, leakage prevention in geologic CO2 sequestration, and hydrogen storage. The extent to which a porous medium yields to external and/or internal (i.e., fluid) loadings, and where/how microscale cracks nucleate and coalesce within its microstructure, govern the emergence of macroscopic fractures, and with it, the evolution of macroscale transport properties. Micron-scale computing plays a key role in both understanding these phenomena and predicting them. However, available models are either too slow, scale poorly with problem size, or are unreliable, meaning a mechanism for estimating and controlling prediction errors is absent. The first part of this talk will propose a mathematical approximation based on domain decomposition and local, physics-based closures. This is then formulated into an algebraic preconditioner that renders the approach portable across existing software and numerical methods (FEM, FVM). Extensive tests demonstrate superior performance against other preconditioners, such as algebraic multigrid, in complex 2D/3D geometries with pre-existing and evolving cracks. As a brief segue, we will discuss how these ideas extend to solving the Navier-Stokes equation, which has a saddle-point structure, thus subsuming and outperforming established approximations such as the "pore-network method." Time permitting, the role of machine learning in achieving further acceleration will be discussed and the existence of a certain kind of trade-off will be highlighted and cautioned. The second part of the talk will focus on what it takes to build a reduced-order model for crack nucleation and failure, achieving orders of magnitude more in speed. The idea is to foreshadow where cracks might nucleate and to devise an algorithm that incurs only an offline cost with minimal online overhead. The "foreshadowing" is based on a set of hypotheses that will be supported by experimental observations. The result is the tractability of very large domain sizes encountered in practice. The price for this added speed is a partial lost in the ability to control errors.

Bio: Yashar Mehmani is an assistant professor in the Department of Energy and Mineral Engineering (EME) at Penn State University. He is also a co-funded faculty of the Institutes of Energy and the Environment (IEE) at Penn State, and an affiliate of the Penn State Institute for Computational and Data Sciences (ICDS). He did his undergraduate education at Sharif University of Technology in Iran, and his PhD at the University of Texas at Austin, both in Petroleum Engineering. Following that, Yashar was a postdoctoral fellow and later a research scientist at the Energy Resources Engineering Department at Stanford University (2015-2020). His research focuses broadly on the fundamental physics of fluid flow and solid deformation in porous materials related to energy and environmental systems.

NOTE: At this time, in-person Mechanical and Civil Engineering Lectures are open to all Caltech students/staff/faculty/visitors.