Peridynamic differential operator and its applications
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Speaker: Erdogan Madenci, Aerospace and Mechanical Engineering, University of Arizona
Title: Peridynamic differential operator and its applications
Abstract: Peridynamic (PD) differential operator (PDDO) converts the existing governing field equations from their local to nonlocal form while introducing an internal length parameter. The PDDO 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 problem when addressing discontinuities. Although the PD theory is extremely suitable to model the response of structures involving crack initiation and propagation at multiple sites, with arbitrary paths, it is also applicable to other field equations involving phase change arising from corrosion and electrodeposition. Furthermore, it is applicable to hyperbolic equations for which the solution does not smooth out with time and discontinuities persist such as a shock wave. Lastly, the PDDO enables the evaluation of derivatives of any order in a multi-dimensional space, and provides a unified approach to transfer information within a set of discrete data, and among data sets. This presentation provides an overview of the PD concept, the derivation of the PDDO, and applications concerning data reduction and recovery, solutions to complex partial differential equations, failure prediction in structural materials under complex loading conditions.