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Article overview
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Parallel three-dimensional simulations of quasi-static elastoplastic solids. Part II: Coordinate transformations | | Nicholas M. Boffi
; Chris H. Rycroft
; | | Date: |
8 Apr 2019 | | Abstract: | In this two-part paper, we extend to three dimensions a new projection method
for simulating hypo-elastoplastic solids in the quasi-static limit. The method
is based on a surprising mathematical correspondence to the incompressible
Navier-Stokes equations, where the projection method of Chorin (1968) is an
established numerical technique. In both parts, we explore the method through
numerical simulation of a three-dimensional continuum-level elastoplastic model
of a bulk metallic glass, based on the shear transformation zone (STZ) theory
of amorphous plasticity.
Here in part II, we present a variation of the projection method based on a
coordinate transformation that enables the implementation of boundary
conditions through deformation of the grid itself. By considering physically
equivalent situations, we show that the original quasi-static method and the
transformed method agree up to small differences in discretization errors that
shrink as the grid spacing is decreased. We demonstrate how this formalism can
be used to implement several interesting cases with ease, such as Lees-Edwards
boundary conditions commonly used in molecular-dynamics simulations, and pure
shear boundary conditions. | | Source: | arXiv, 1904.4145 | | Services: | Forum | Review | PDF | Favorites | |
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