A simple alteration of the peridynamics correspondence principle to eliminate zero-energy deformation

TL;DR

This paper proposes a simple modification to the peridynamics correspondence principle using sub-horizons to effectively eliminate zero-energy deformation modes while maintaining stability and minimal deviation from the original model.

Contribution

It introduces a novel sub-horizon based approach to eliminate zero-energy modes in peridynamics, improving stability with minimal changes to the original formulation.

Findings

Sub-horizon method effectively reduces zero-energy deformation modes.

Numerical simulations confirm the stability and efficacy of the proposed approach.

The approach maintains close adherence to the original correspondence model.

Abstract

We look for an enhancement of the correspondence model of peridynamics with a view to eliminating the zero-energy deformation modes. Since the non-local integral definition of the deformation gradient underlies the problem, we initially look for a remedy by introducing a class of localizing corrections to the integral. Since the strategy is found to afford only a reduction, and not complete elimination, of the oscillatory zero-energy deformation, we propose in the sequel an alternative approach based on the notion of sub-horizons. A most useful feature of the last proposal is that the setup, whilst providing the solution with the necessary stability, deviates only marginally from the original correspondence formulation. We also undertake a set of numerical simulations that attest to the remarkable efficacy of the sub-horizon based methodology.