An extended ordinary state-based peridynamics for non-spherical horizons

TL;DR

This paper introduces an extended ordinary state-based peridynamics model that accommodates non-spherical horizons, enabling more accurate and flexible simulation of complex fracture behaviors without volume correction.

Contribution

The paper develops the XOSBPD model that removes the spherical horizon limitation and allows arbitrary horizon shapes with non-uniform discretization, enhancing fracture analysis capabilities.

Findings

Accurate simulation of complex dynamical fractures.

No need for volume or surface correction.

Supports non-uniform discretization with various horizon sizes.

Abstract

This work presents an extended ordinary state-based peridynamics (XOSBPD) model for the non-spherical horizons. Based on the OSBPD, we derive the XOSBPD by introducing the Lagrange multipliers to guarantee the non-local dilatation and non-local strain energy density (SED) are equal to local dilatation and local SED, respectively. In this formulation, the XOSBPD removes the limitation of spherical horizons and is suitable for arbitrary horizon shapes. In addition, the presented XOSBPD does not need volume and surface correction and allows non-uniform discretization implementation with various horizon sizes. Three classic examples demonstrate the accuracy and capability for complex dynamical fracture analysis. The proposed method provides an efficient tool and in-depth insight into the failure mechanism of structure components and solid materials.