Reduction of 3D axisymmetric models to 2D in peridynamics

Abstract: Introduced by Silling in 2000, peridynamics provides an alternative approach to model deformations of solid materials, in particular deformations concerning failure and damage, using integral equations rather than partial differential equations commonly employed in the classical theory of continuum mechanics. In peridynamic simulations of material failure, cracks appear naturally and propagate as a consequence of bond breaking between material points.

In this talk, we consider axisymmetric problems where the geometry, external loading, and body forces are invariant under rotation about a given axis of symmetry, resulting in an axisymmetric deformation of all material points. We start with a full 3D peridynamic model with a linear pairwise force function. Exploiting axisymmetry, we incorporate the contribution of out-of-plane bond forces into the in-plane pairwise force function and derive a 2D model on a representative half plane passing through the axis of symmetry. This results in a significant reduction of computational cost. We also revisit the classical theory of linear elasticity in the axisymmetric setup and compare it with our results numerically.

Biography: Debdeep Bhattacharya is a Ph.D. candidate in Applied Mathematics at the George Washington University. He is co-advised by Prof. Frank Baginski (George Washington University) and Prof. Svetlana Roudenko (Florida International University). His research interests include nonlinear partial differential equations, harmonic analysis and signal processing.