Seamless Coupling of Peridynamics with Finite Element Method for the Simulation of Material Failure and Damage

Abstract

Peridynamic (PD) theory, based on the concept of material point interactions over a finite distance through long-range forces, results in the integral form of the equation of motion. It offers a uniform mathematical framework suitable for analyzing the mechanics of diverse systems, from discrete entities to continuous or discontinuous media. This feature allows for damage nucleation at multiple, unspecified sites and its propagation along complex, unguided paths. The finite element method (FEM) accurately predicts material deformation using existing constitutive models while incorporating specific fracture criteria for damage propagation. However, these criteria rely on local stress and strain fields and are significantly influenced by mesh size, limiting their accuracy. Additionally, predicting damage can be cumbersome due to undefined displacement derivatives at discontinuities. Although PD theory is highly effective for failure prediction, it incurs higher computational costs compared to FEM due to its nonlocal nature. Therefore, integrating PD with FEM to capitalize on their respective advantages is a key motivation. Coupling PD and FEM presents challenges due to the nonlocal nature of PD with volume constraints and the local nature of FEM with surface constraints. This study introduces a framework for conducting single- and dual-horizon bond-based (BB), ordinary state-based (OSB), and non-ordinary state-based (NOSB) PD analysis within ANSYS, utilizing its native MATRIX27 elements. Traditional PD models assume a single horizon, leading to spurious wave reflections and ghost forces in non-uniform meshes. The dual horizon PD concept allows for non-uniform discretization. The coupling approach uses the weak form of PD governing equations, integrating PD and FE regions by sharing the same nodes along their interface without overlap or constraint conditions. The PD domain is divided into three regions to ensure equilibrium equations are satisfied and to impose boundary conditions directly, eliminating the need for a fictitious layer. Failure mechanisms are introduced gradually with dynamic updates to MATRIX27 element coefficients. This study also introduces the coupling of BB, OSB, and NOSB PD models with traditional FE elements in ANSYS for structures with initial strain, considering a known temperature profile and capturing the effect of thermal strain on the coupled PD-FE model's response. Finally, it introduces the PD-FE coupling methodology to model structural response in the presence of geometric and material nonlinearity. The solution to the governing equations is achieved through implicit solution methods. The accuracy of this approach is validated by comparing it with results from finite element analysis in scenarios without failure for quasi-static and dynamic analysis. The comparisons indicate excellent agreement under plane stress and plane strain assumptions, including quasi-static and dynamic loading conditions.