A peridynamic Reissner-Mindlin shell theory

In this work, we have developed a state-based peridynamics theory for nonlinear Reissener-Mindlin shells to model and predict large deformation of shell structures with thick wall. The nonlocal peridynamic theory of solids offers an integral formulation that is an alternative to traditional local continuum mechanics models based on partial differential equations. This formulation is applicable for solving the material failure problems involved in discontinuous displacement fields. The governing equations of the state-based peridynamic shell theory are derived based on the nonlocal balance laws by adopting the kinematic assumption of the Reissner and Mindlin plate and shell theories. In the numerical calculations, the stress points are employed to ensure the numerical stability. Several numerical examples are conducted to validate the nonlocal structure mechanics model and to verify the accuracy as well as the convergence of the proposed shell theory.