Seminars
Prof. David Kamensky
Mechanical and Aerospace Engineering Department
University of California, San Diego
Isogeometric and Meshfree Analysis of Nonlocal Damage, Fracture, and Contact---Part I: Implementation and Application
ABSTRACT:Fracture and contact entail topology changes in the domains over which solid and structural mechanics problems are posed. These topology changes are awkward (at best) to include in classical local models of continua. There is a long history of researchers introducing a length scale into damage and fracture formulations, to obtain better-behaved nonlocal regularizations. Recently, I have also begun to explore nonlocal regularizations of contact mechanics. Meshfree numerical methods that represent material configurations as point clouds provide the geometric flexibility needed to simulate topological events, and are therefore a natural class of approaches to use. It may be less clear why one would consider isogeometric approaches for these problems, since they represent discrete solutions in spaces that are even more regular than those of traditional finite element methods. However, I will demonstrate several interesting examples of synergy between isogeometric and meshfree methods for approximating nonlocal regularizations of damage, fracture, and contact: Meshfree--isogeometric fluid--structure interaction with phase-field fracture, isogeometric analysis of gradient-enhanced damage in composite shell structures, and meshfree computation of nonlocal contact forces in isogeometric analysis of heart valves. While much of this work was done using custom research codes, I have also begun developing accessible open-source isogeometric analysis, leveraging finite element automation software from the FEniCS Project. Will it be possible, in the future, to bring similar automation to meshfree methods?
An immediately-following computational and applied mathematics seminar will elaborate on certain interesting mathematical details of the methods used in this work.
BIOGRAPHY: David Kamensky is an Assistant Professor in the Mechanical and Aerospace Engineering department at UC San Diego, specializing in computational mechanics. He received a BS from the University of Virginia in 2011, where he studied Computer Science and Physics, and a PhD from the University of Texas at Austin in 2016, in Computational Science, Engineering, and Mathematics. Before joining the faculty at UC San Diego in 2019, he held postdoctoral positions in the Structural Engineering department at UC San Diego and in the School of Engineering at Brown University.