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The imposition of nonconforming boundary condition in the MPM remains a challenge as the MPM discretizes the material domain with material points which do not locate at the physical boundary. Therefore, the existing strategies to impose such boundary conditions always aim to track, reconstruct, or represent the material boundary positions which increase simulation complexity when dealing with boundaries that undergo large deformations or undergo fracture, especially in 3D.

A novel strategy, named virtual stress boundary (VSB), is proposed to apply nonconforming Neumann boundary condition without requiring the exact boundary position. The VSB transform an original problem with a nonconforming traction boundary condition into an equivalent problem with a prescribed virtual stress field which can produce the exact same response within the material domain. Then a modified governing equation without boundary representation is subsequently constructed and the volume integral terms are computed by both particle quadrature and cell quadrature. Several numerical examples are investigated to assess the accuracy and demonstrate the capability of the proposed approach in simulating different engineering problems. These numerical examples include mesh refinement to illustrate the method’s good convergence and a 3D complex surface to illustrate the method’s capability. Beises, the VSB is utilized to model the reservoir interactions in simulating the well-known case study of the earthquake-induced Lower San Fernando Dam (LSFD) failure which can predict improved kinematic behavior and post-failure cross-sectional features.