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Methodology - Particle Method

The smoothed particle Galerkin (SPG) [1] combines nodal integration with displacement smoothing scheme to be an efficient and stable method for extremely large deformation and material failure analysis. [2] Different from the conventional FEM where the element erosion technique is utilized to mimic the material separation, SPG introduces a bond-based material failure criterion to reproduce the strong discontinuity in displacement field without sacrificing the conservation properties of the system equations. [3]

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  • Advantage

    • No parameter to be tuned for numerical stabilization

    • Flexible to be coupled with FEM

    • Time step size is not decreased in severe material deformation

    • Bond-based failure model without eroding damaged material

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  • Current implementation [ex]

    • 3D solid

      • FEM solid mesh as input: TET, HEX and PENT​

    • Semi-brittle and ductile material failure [kw]

    • Multiple types of particle kernel for different failure mode​s [4][kw]

    • Particle-based multi-body/self contact [kw]

    • Immersed SPG for fiber-reinforced composite [5][kw]

    • Thermal-mechanical coupling

    • Explicit analysis

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  • Limitation

    • High cost in CPU time and memory

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