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Parallel three-dimensional simulations of quasi-static elastoplastic solids. Part I: Numerical formulation and examples | | 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 model of a bulk
metallic glass, based on the shear transformation zone (STZ) theory of
amorphous plasticity.
Here in part I, we review the development of the quasi-static projection
method, and extend it to three dimensions. We discuss the development of a
three-dimensional parallel geometric multigrid solver employed to solve a
linear system for the quasi-static projection. We test the method by simulating
three-dimensional shear band nucleation and growth in materials undergoing
simple shear, and explore the agreement of the method with an explicit
timestepping method as the quasi-static limit is mathematically approached. We
consider several three-dimensional examples and contrast the dynamics of shear
banding in these situations with previous two-dimensional studies. We consider
the generation of physically realistic randomly distributed initial conditions
in a relevant STZ internal variable, and discuss relevance to experimental
studies of shear banding. | | Source: | arXiv, 1904.3808 | | Services: | Forum | Review | PDF | Favorites | |
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