Coupled systems mechanics

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Localized particle boundary condition enforcements for the state-based peridynamics

  • Wu, C.T. (Livermore Software Technology Corporation) ;
  • Ren, Bo (Department of Civil and Environmental Engineering, University of California)
  • Received : 2014.11.24
  • Accepted : 2015.03.08
  • Published : 2015.03.25
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Abstract

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

Keywords

Acknowledgement

Supported by : LSTC

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