Multiphysics Simulations Using Peridynamics Differential Operator

Dr. Erdogan Madenci

Professor

Department of Aerospace and Mechanical Engineering 

Unviersity of Arizona

madenci@arizona.edu

About Dr. Erdogan Madenci

Prof. Erdogan Madenci has been a professor in the Department of Aerospace and Mechanical Engineering at the University of Arizona since 1989. He received his B.S. degrees on both Mechanical and Industrial engineering in 1980 and 1981, respectively. He then received his M.S. degree in Applied Mechanics from Lehigh University, Bethlehem, PA in 1982. He earned his Ph.D. degree in Engineering Mechanics from the University of California, Los Angeles in 1987. Prior to joining the University of Arizona, he worked at Northrop Corporation, Aerospace Corporation, and the Fraunhofer Institute. He has also worked at the KTH Royal Institute of Technology, NASA Langley Research Center, Sandia National Labs and MIT as part of his sabbatical leaves.
 
Prof. Madenci is the lead author of five books on Peridynamics (also available in Chinese) and Finite Element analysis. He serves as the Co-Editor-in-Chief of the Journal of Peridynamics and Nonlocal Modeling and an Associate Editor of ASME Open Journal of Engineering. He is a Fellow of ASME and an Associate Fellow of AIAA.

Abstract

Peridynamics (PD) converts the existing governing field equations from their local to nonlocal form through the PD differential operator while introducing an internal length parameter. The PD differential operator enables differentiation through integration. As a result, the equations become valid everywhere regardless of discontinuities. The lack of an internal length parameter in the classical form of the governing equations is the source of problems when addressing crack initiation and propagation. Although PD is extremely suitable to model the response of structures involving discontinuities, fractures, and other complex phenomena, it is also applicable to other fields, including thermal diffusion, moisture diffusion, electric potential distribution, vacancy diffusion, and neutronic diffusion in either an uncoupled or a coupled manner. This presentation provides an overview of the PD concept, the derivation of the PD differential operator, and multiphysics applications by considering different field equations coupled among themselves or coupled with the deformation field such as hygrothermomechanics, hydromechanics, corrosion and electrodeposition and electromigration.