Generalized reproducing kernel peridynamics: unification of local and non-local meshfree methods, non-local derivative operations, and an arbitrary-order state-based peridynamic formulation

• DOI: 10.1007/s40571-019-00266-9
• Publication Date: 2019-09-04T13:04:42Z
• Authors: Michael Hillman; Marco Pasetto; Guohua Zhou
• Keywords: Peridynamics; Meshfree methods; Kernel (algebra); Collocation (remote sensing)

State-based peridynamics is a non-local reformulation of solid mechanics that replaces the force density divergence stress with an integral action states on bonds local to given position, which precludes differentiation aim model strong discontinuities effortlessly. A popular implementation meshfree formulation where discretized by quadrature points, results in series unknowns at points under strong-form collocation framework. In this work, discretization state-based correspondence principle examined and compared traditional methods based classical mechanics. It first shown way peridynamic approximates can be unified implicit gradient approximation, termed reproducing kernel approximation. This allows construction deformation gradients arbitrary-order accuracy, as well approximations higher-order derivatives. high-order accurate then proposed replace original peridynamics, order obtain global accuracy numerical solution. These two operators used conjunction one another method. The version method tested against benchmark solutions examine verify convergence properties exhibit superconvergent behavior nodal setting.