A generalized essentially non-hourglass total Lagrangian SPH solid dynamics
CoRR(2024)
摘要
In this paper, we tackle a persistent numerical instability within the total
Lagrangian smoothed particle hydrodynamics (TLSPH) solid dynamics.
Specifically, we address the hourglass modes that may grow and eventually
deteriorate the reliability of simulation, particularly in the scenarios
characterized by large deformations. We propose a generalized essentially
non-hourglass formulation based on volumetric-deviatoric stress decomposition,
offering a general solution for elasticity, plasticity, anisotropy, and other
material models. Comparing the standard SPH formulation with the original
non-nested Laplacian operator applied in our previous work
to handle the hourglass issues in standard elasticity,
we introduce a correction for the discretization of shear stress that relies on
the discrepancy produced by a tracing-back prediction of the initial
inter-particle direction from the current deformation gradient. The present
formulation, when applied to standard elastic materials, is able to recover the
original Laplacian operator. Due to the dimensionless nature of the correction,
this formulation handles complex material models in a very straightforward way.
Furthermore, a magnitude limiter is introduced to minimize the correction in
domains where the discrepancy is less pronounced. The present formulation is
validated, with a single set of modeling parameters, through a series of
benchmark cases, confirming good stability and accuracy across elastic,
plastic, and anisotropic materials. To showcase its potential, the formulation
is employed to simulate a complex problem involving viscous plastic Oobleck
material, contacts, and very large deformation.
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