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Title: Parallel three-dimensional simulations of quasi-static elastoplastic solids

Abstract

Hypo-elastoplasticity is a flexible framework for modeling the mechanics of many hard materials under small elastic deformation and large plastic deformation. Under typical loading rates, most laboratory tests of these materials happen in the quasi-static limit, but there are few existing numerical methods tailor-made for this physical regime. Here, we extend to three dimensions a recent projection method for simulating quasi-static hypo-elastoplastic materials. The method is based on a mathematical correspondence to the incompressible Navier–Stokes equations, where the projection method of Chorin (1968) is an established numerical technique. We develop and utilize a three-dimensional parallel geometric multigrid solver employed to solve a linear system for the quasi-static projection. Our method is tested through simulation of three-dimensional shear band nucleation and growth, a precursor to failure in many materials. As an example system, we employ a physical model of a bulk metallic glass based on the shear transformation zone theory, but the method can be applied to any elastoplasticity model. We consider several examples of three-dimensional shear banding, and examine shear band formation in physically realistic materials with heterogeneous initial conditions under both simple shear deformation and boundary conditions inspired by friction welding.

Authors:
 [1];  [2]
  1. Harvard Univ., Cambridge, MA (United States)
  2. Harvard Univ., Cambridge, MA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1580840
Alternate Identifier(s):
OSTI ID: 1809395
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Computer Physics Communications
Additional Journal Information:
Journal Volume: 257; Journal ID: ISSN 0010-4655
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; fluid mechanics; Chorin-type projection method; plasticity; elastoplasticity

Citation Formats

Boffi, Nicholas M., and Rycroft, Chris H.. Parallel three-dimensional simulations of quasi-static elastoplastic solids. United States: N. p., 2020. Web. https://doi.org/10.1016/j.cpc.2020.107254.
Boffi, Nicholas M., & Rycroft, Chris H.. Parallel three-dimensional simulations of quasi-static elastoplastic solids. United States. https://doi.org/10.1016/j.cpc.2020.107254
Boffi, Nicholas M., and Rycroft, Chris H.. Sun . "Parallel three-dimensional simulations of quasi-static elastoplastic solids". United States. https://doi.org/10.1016/j.cpc.2020.107254. https://www.osti.gov/servlets/purl/1580840.
@article{osti_1580840,
title = {Parallel three-dimensional simulations of quasi-static elastoplastic solids},
author = {Boffi, Nicholas M. and Rycroft, Chris H.},
abstractNote = {Hypo-elastoplasticity is a flexible framework for modeling the mechanics of many hard materials under small elastic deformation and large plastic deformation. Under typical loading rates, most laboratory tests of these materials happen in the quasi-static limit, but there are few existing numerical methods tailor-made for this physical regime. Here, we extend to three dimensions a recent projection method for simulating quasi-static hypo-elastoplastic materials. The method is based on a mathematical correspondence to the incompressible Navier–Stokes equations, where the projection method of Chorin (1968) is an established numerical technique. We develop and utilize a three-dimensional parallel geometric multigrid solver employed to solve a linear system for the quasi-static projection. Our method is tested through simulation of three-dimensional shear band nucleation and growth, a precursor to failure in many materials. As an example system, we employ a physical model of a bulk metallic glass based on the shear transformation zone theory, but the method can be applied to any elastoplasticity model. We consider several examples of three-dimensional shear banding, and examine shear band formation in physically realistic materials with heterogeneous initial conditions under both simple shear deformation and boundary conditions inspired by friction welding.},
doi = {10.1016/j.cpc.2020.107254},
journal = {Computer Physics Communications},
number = ,
volume = 257,
place = {United States},
year = {2020},
month = {3}
}

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