J.S. Chen, Jonghyuk Baek, and Kristen Susuki, University of California-San Diego

Abstract:

The localized intensive deformation in the damaged solids requires highly refined discretization for accurate prediction, which significantly increases the computational cost. While adaptive model refinement can be employed for enhanced effectiveness, it is cumbersome for the traditional mesh-based methods to perform adaptive model refinement in modeling the evolving localizations. In this work, neural network (NN)-enriched meshfree approximations for modeling strain localization is proposed, where the location, orientation, and the shape of the solution transition near localization is automatically captured by the NN approximation via the minimization of total potential energy. The standard RKPM or Isogeometric Analysis is then utilized to approximate the smooth part of the solution to permit a much coarser discretization than the high-resolution discretization needed to capture sharp solution transition with the conventional methods. The proposed neural network approximation is regularized by introducing a length scale related to the objective dissipation energy. The effectiveness of the proposed NN-RKPM is verified by a series of numerical examples, including shearband localization, damage propagation, and grain refinement simulations. The potential applications to NN-based enrichment to finite element approximations for localization problems will also be highlighted.

Biography:

J. S. Chen is the William Prager Chair Professor of Structural Engineering Department and Aerospace Engineering Department at UC San Diego. Before joining UCSD in October 2013, he was the Chancellor’s Professor of UCLA Civil & Environmental Engineering Department where he served as the Department Chair during 2007-2012. J. S. Chen’s research is in computational mechanics and multiscale materials modeling with specialization in the development of meshfree methods. He is the Past President of US Association for Computational Mechanics (USACM) and the Past Present of ASCE Engineering Mechanics Institute (EMI). He has received numerous awards, including the Grand Prize from Japan Society for Computational Engineering and Science (JSCES), Computational Mechanics Award from International Association for Computational Mechanics (IACM), ICACE Award from International Chinese Association for Computational Mechanics (ICACM), the Ted Belytschko Applied Mechanics Award from ASME Applied Mechanics Division, the Belytschko Medal from U.S. Association for Computational Mechanics (USACM), Computational Mechanics Award, Japan Association for Computational Mechanics (JACM), among others. He is the Fellow of USACM, IACM, ASME, EMI, SES, ICACM, and ICCEES.