Virtual stress boundary method to impose nonconforming Neumann boundary condition

  • Liang, Yong (Xi'an Jiaotong University)
  • Given, Joel (University of Caliafornia, Berkeley)
  • Chandra, Bodhinanda (University of Caliafornia, Berkeley)
  • Zhang, Xiong (Tsinghua University)
  • Soga, Kenichi (University of Caliafornia, Berkeley)

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The imposition of boundary condition in the MPM remains a challenge since its original formulation was proposed. the previously developed methods to apply nonconforming boundary condition are mainly focusing on how to track, reconstruct, or represent the material boundary positions. These approaches increase simulation complexity when dealing with boundaries that undergo large deformations or undergo fracture, especially in 3D. In the current work, a novel strategy to apply nonconforming Neumann boundary condition is proposed that does not require the exact boundary position. The original problem with a nonconforming traction boundary condition is transformed into an equivalent problem with a prescribed virtual stress field. Importantly, both the original and the transformed problems produce the exact same response within the material domain. To solve the equivalent problem, a modified governing equation without boundary representation is subsequently constructed, where the volume integral terms are computed by both particle quadrature and cell quadrature. Besides, the coupling with the high-order MPM including the GIMP, BSMPM and LME further improves the accuracy. 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.