Coupled peridynamic and finite element analysis for nonlinear material response with finite deformation

Although nonlocal peridynamic (PD) theory is highly effective for predicting material failure, it incurs higher computational costs than the finite element method (FEM). This motivates the integration of PD with FEM to leverage their respective advantages. However, coupling PD and FEM is challenging due to PD's nonlocal volume constraints and FEM's local surface constraints. Existing coupling techniques address these challenges for linear elastic materials under small deformations. This study introduces a PD-FE coupling method to model structural response under geometric and material nonlinearity. The PD domain can be fully or partially enclosed by finite elements, sharing common interface nodes without additional constraints or overlapping zones typically used for interface management. The variational form of the coupled PD-FE equilibrium equations is derived using the principle of virtual power, and nonlinear governing equations are solved implicitly. PD force density vectors and tangent stiffness matrices are formulated using the PD correspondence principle. The nonlinear equations are solved via the Newton-Raphson method to compute incremental displacements under load changes. For nonlinear transient analysis, the Newmark time integration scheme is employed. The proposed approach is validated by analyzing the finite deformation response of a polymer layer modeled as a nearly incompressible Neo-Hookean material under quasi-static and transient loading. The analysis is conducted under both plane stress and plane strain conditions.