Then, we develop an efficient n-th order symmetrical variationally consistent nodal integration scheme for RK enhanced weak form peridynamics. Next, we introduce an RK approximation to the field variables in strong form peridynam-ics to increase the order of convergence of peridynamic numerical solutions. Scheme to transition from the computationally cheaper Lagrangian RKPM to the semi-Lagrangian RKPM. The latter can be recovered through the use of the peridynamic weak form, which however involves costly double integration.įirst, we first propose, in the context of local mechanics, a blending-based spatial coupling This approach is limited to first order convergence and often lacks the symmetry of interaction of the continuous form. In engineering applications, a simple node-based discretization of peridynamics is typically employed. The peridynamic nonlocal theory circumvents these issues by reformulating solid mechanics in terms of integral equations. Many challenges, such as the need of accurately representing the singular stress field at crack tips. This, however, results in a highįurthermore, for crack propagation problems, the use of classical local mechanics presents Not require the deformation gradient to be positive definite. Mentation, as by reconstructing the field approximations in the current configuration it does Method (RKPM) has been proved to be particularly effectively for material damage and frag. In the framework of local mechanics, the semi-Lagrangian reproducing kernel particle Meshing due to excessive mesh distortion. Some of the common issues associated with mesh-based techniques, such as the need for re. For these classes of problems, meshfreeĭiscretizations of local and nonlocal approaches, have been shown to be effective as they avoid Remains a challenge in computational mechanics. Of problems involving large deformations, material fragmentation and crack propagations still Achieving good accuracy while keeping a low computational cost in numerical simulations
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