A Peridynamic View of Classical Continuum Mechanics

Abstract

Peridynamics is a formulation of the classical elastic theory that was originally targeted at simulating deformable objects with discontinuities, especially fractures. In this talk, I will introduce how to reformulate classical continuum mechanics with the peridynamic theory. To get an intuitive model that can be easily controlled, we formulate the strain energy density function as a function parameterized by the dilatation and bond stretches, which can be decomposed into multiple one-dimensional functions independently. To account for nonlinear material behaviors, we also propose a set of nonlinear basis functions to help design a nonlinear strain energy function more easily. For an anisotropic material, we additionally introduce an anisotropic kernel to control the elastic behavior for each bond independently. Experiments show that our model is flexible enough to approximately regenerate various hyperelastic materials in classical elastic theory, including St.Venant-Kirchhoff and Neo-Hookean materials.

Biography

Prof. Xiaowei He is currently an associate professor at the Institute of Software, Chinese Academy of Sciences. He received both his BS and MS degrees from Peking University, and his Ph.D. from Institute of Software, Chinese Academy of Sciences. His research interests are mainly focused on computer graphics, computational physics, smoothed particle hydrodynamics, peridynamics and nolocal theory. In recent years, he has published several papers in international journals/conferences including SIGGRAPH, TVCG, SCA, etc. Among them, he proposed an efficient phase-field-based fluid solver to simulate arbitrarily complex multi-phase flows, which was adopted by Adobe to realize a real-time three-dimensional oil painting system. Recently, he has been doing research on how to apply machine learning to help improve both the performance and accuracy over traditional numerical solvers. He received two grants as PI from the Natural Science Foundation of China (NSFC) in 2014 and 2018, respectively.