Nonlocal continuum damage modeling for functionally graded plates of third-order shear deformation theory

This article presents an effective computational approach that incorporates a quasi-brittle damage model into the isogeometric analysis of plates made of functionally graded materials. The plate kinematics is represented by a third-order shear deformation theory for higher accuracy. A coupling nonlocal equivalent strain field is introduced on the plate neutral surface to control the softening behavior. The utilization of the neutral surface in functionally graded plates enables the use of a single damage parameter over each plate cross-section. As a consequence, plate stiffness matrices can be calculated analytically, which simplifies the proposed damage model and its computer implementation. The discretization of the problem domain is based on basis functions generated from the non-uniform rational B-splines (NURBS) which are used for both geometric representation and field variable approximations, i.e., displacement and nonlocal equivalent strain. Owing to the high-order continuity of the NURBS basis functions, local features such as fracture damage zones can be resolved accurately. The performance of the proposed approach is demonstrated through several numerical examples under different loading configurations and compared with results from other approaches.