Tensor-involved peridynamics: A unified framework for isotropic and anisotropic materials

TL;DR

This paper presents a tensor-involved peridynamics framework that unifies the simulation of isotropic and anisotropic materials, enhancing stability and accuracy, and introduces a damage model validated by crack propagation experiments.

Contribution

The paper introduces a novel tensor-involved peridynamics model that extends traditional frameworks to handle anisotropic materials with improved stability and includes a damage model for crack prediction.

Findings

Model ensures stability for anisotropic materials without extra corrections.

Numerical experiments confirm accuracy and stability across scenarios.

Damage model accurately predicts crack paths in 2D plates.

Abstract

In this paper, we introduce tensor involved peridynamics, a unified framework for simulating both isotropic and anisotropic materials. While traditional peridynamics models effectively simulate isotropic materials, they face challenges with anisotropic materials and are prone to instability caused by zero energy modes. Our novel model extend the linear bond based peridynamics framework by incorporating the elastic tensor into the micrmodulus function, thereby ensuring stability for anisotropic materials without the need for additional corrections. For isotropic materials. the model mantains compatibility with conventional bond based peridynamics, assuming Possion's rations of 1/4 in 3D and 1/3 in 2D.Numerical experiments confirm the model's stability and accuracy across various scenarios. Additionally, we introduce a damage model for isotropic materials. validating its performance in predicting crack propagation paths in a 2D plate. The results show superior alignment with experimental date compared to traditional model.