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

In this paper, we present a novel bond-based peridynamic model, termed Tensor-Involved Peridynamics (Ti-PD), which offers a unified framework for simulating both isotropic and anisotropic materials. This model enhances the conventional linear bond-based peridynamics by integrating a fourth-order tensor into the micromodulus function. The tensor components are calibrated to ensure the peridynamic equations converge to the classical continuum elasticity equations as the horizon parameter approaches zero. For isotropic materials with Poisson’s ratios of 1/4 in three dimensions and 1/3 in two dimensions with plane stress condition, the Ti-PD model aligns exactly with traditional bond-based peridynamics. To further expand its applicability, we introduce a damage model specifically designed for isotropic materials, incorporating a novel critical stretch criterion distinct from ordinary state-based peridynamics. The effectiveness of the Ti-PD model in simulating general anisotropic materials is demonstrated through numerical experiments. Additionally, the damage model is validated via simulations of crack propagation in a two-dimensional plate, showcasing superior agreement with experimental data compared to conventional ordinary state-based peridynamics.