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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.

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