Tensor-Involved Peridynamics: A Unified Framework for Isotropic and Anisotropic Materials

Abstract

In this paper, we introduce tensor-involved Peridynamics, a unified framework for simulating both isotropic and anisotropic materials. While traditional peridynamic models effectively simulate isotropic materials, they face challenges with anisotropic materials and are prone to instability caused by zero-energy modes. Our novel model extends the linear bond-based peridynamics framework by incorporating the elastic tensor into the micromodulus function, thereby ensuring stability for anisotropic materials without the need for additional corrections. For isotropic materials, the model maintains compatibility with conventional bond-based peridynamics, assuming Poisson’s ratios 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 data compared to traditional models.

Keywords: ridynamics, Anisotropic materials, Elastic tensor, Zero-energy mode