Improvements to the Prototype Micro-Brittle Linear Elasticity Model of Peridynamics

TL;DR

This paper improves the accuracy of the prototype micro-brittle Peridynamics model by proposing a correction to the discretization errors, enabling better modeling of complex geometries and crack propagation.

Contribution

A correction method for the discretization errors in the PMB Peridynamics model is proposed, enhancing accuracy and allowing for non-homogeneous discretizations in complex geometries.

Findings

Corrected model accurately predicts sound wave velocities.

Corrected model reproduces crack initiation and growth.

Original model overestimates wave velocities.

Abstract

This paper assesses the accuracy and convergence of the linear-elastic, bond-based Peridynamic model with brittle failure, known as the prototype micro-brittle (PMB) model. We investigate the discrete equations of this model, suitable for numerical implementation. It is shown that the widely used discretization approach incurs rather large errors. Motivated by this observation, a correction is proposed, which significantly increases the accuracy by cancelling errors associated with the discretization. As an additional result, we derive equations to treat the interactions between differently sized particles, i.e., a non-homogeneous discretization spacing. This presents an important step forward for the applicability of the PMB model to complex geometries, where it is desired to model interesting parts with a fine resolution (small particle spacings) and other parts with a coarse resolution in order to gain numerical efficiency. Validation of the corrected Peridynamic model is performed by comparing longitudinal sound wave propagation velocities with exact theoretical results. We find that the corrected approach correctly reproduces the sound wave velocity, while the original approach severely overestimates this quantity. Additionally, we present simulations for a crack growth problem which can be analytically solved within the framework of Linear Elastic Fracture Mechanics Theory. We find that the corrected Peridynamics model is capable of quantitatively reproducing crack initiation and propagation.