Peridynamic Beams and Plates: A Non-Ordinary State-Based Model

Abstract

While multiple peridynamic material models capture the behavior of solid materials, not all structures are conveniently analyzed as solids. Finite Element Analysis often uses 1D and 2D elements to model thin features that would otherwise require a great number of 3D elements, but peridynamic thin features remain underdeveloped despite great interest in the engineering community. This work presents non-ordinary state-based peridynamic models for the simulation of thin features. Beginning from an example non-ordinary state-based model proposed by Silling in 2007, lower dimensional peridynamic models of beams and plates are developed and shown to be energy equivalent to classical models for well-behaved deformations. The resulting plate model is initially restricted to a Poisson’s ratio of ν = 1/3, but is extended to arbitrary Poisson’s ratio via a bending state decomposition. Simple test cases demonstrate the model’s performance.