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Kinematic constraints in the state-based peridynamics with mixed local/nonlocal gradient approximations. (English) Zbl 1311.74019
Summary: In contrast to the partial differential equation in the classical continuum mechanics, the equation of motion in standard state-based peridynamics utilizes an integral form and follows an anti-symmetric relationship for the pairwise particle forces. As a consequence, the kinematic constraints such as the boundary displacements and the coupling with other numerical methods in state-based peridynamics cannot be prescribed directly on the geometric boundary for solid mechanics applications. In this paper, an enhanced variant of the state-based peridynamics for the numerical simulation of continuum mechanics problems is presented. The method is first devised based on a convex kernel approximation to localize the influence function on the boundary. A mixed local/nonlocal gradient approximation is introduced to the computation of particle equation of motion and allows a direct imposition of kinematic constraint in the analysis model. The new formulation is shown to retain the conservation nature of state-based peridynamics. Three numerical benchmarks are studied in this paper to demonstrate the effectiveness and accuracy of the proposed method.

MSC:
74B05 Classical linear elasticity
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
35Q74 PDEs in connection with mechanics of deformable solids
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