A computational approach to integrate three-dimensional peridynamics and two-dimensional higher-order classical elasticity theory for fracture analysis

Abstract As a nonlocal alternative of classical continuum theory, peridynamics (PD) is mathematically compatible to discontinuities, making it particularly attractive for failure prediction. The PD theory on the other side can be computationally demanding due to its nonlocal interactions. A coupling between PD and refined higher-order finite element method (FEM) integrates their salient features. The present study proposes a computational approach to couple three-dimensional peridynamics with two-dimensional higher-order finite elements based on classical elasticity. The bond-based PD modeling is considered in a region where damage might appear while refined finite element modeling is used for the remaining region. The refined finite elements employed in this study are based on the 2D Carrera Unified Formulation (CUF), which provides 3D-like accuracy with optimized computational efficiency. The coupling between PD and FEM is achieved through the Lagrange multiplier method which permits physical consistency and compatibility at the interface domain. An adaptive convergence check algorithm is also proposed to achieve predetermined accuracy in the solution with minimum computational effort. Simulations of quasi-static tension tests, wedge splitting tests and L-plate cracking tests are carried out for verification. In-depth analysis shows that the present approach can reproduce the linear deformation, material degradation and crack propagation in an effective way.