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An Eulerian projection method for quasi-static elastoplasticity

Journal Article · · Journal of Computational Physics
 [1];  [2];  [3]
  1. Harvard Univ., Cambridge, MA (United States). Paulson School of Engineering and Applied Sciences; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Dept. of Mathematics
  2. Simon Fraser Univ., Burnaby, BC (Canada). Dept. of Mathematics
  3. Weizmann Inst. of Science, Rehovot (Israel). Chemical Physics Dept.
+ Show Author Affiliations
A well-established numerical approach to solve the Navier-Stokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved, which is used to orthogonally project the velocity field to maintain the incompressibility constraint. In this paper, we develop a mathematical correspondence between Newtonian fluids in the incompressible limit and hypo-elastoplastic solids in the slow, quasi-static limit. Using this correspondence, we formulate a new fixed-grid, Eulerian numerical method for simulating quasi-static hypo-elastoplastic solids, whereby the stress is explicitly updated, and then an elliptic problem for the velocity is solved, which is used to orthogonally project the stress to maintain the quasi-staticity constraint. We develop a finite-difference implementation of the method and apply it to an elasto-viscoplastic model of a bulk metallic glass based on the shear transformation zone theory. We show that in a two-dimensional plane strain simple shear simulation, the method is in quantitative agreement with an explicit method. Like the fluid projection method, it is efficient and numerically robust, making it practical for a wide variety of applications. We also demonstrate that the method can be extended to simulate objects with evolving boundaries. Here, we highlight a number of correspondences between incompressible fluid mechanics and quasi-static elastoplasticity, creating possibilities for translating other numerical methods between the two classes of physical problems.
Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1525116
Alternate ID(s):
OSTI ID: 1250020
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 300; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (4)

Manifold learning for coarse-graining atomistic simulations: Application to amorphous solids journal August 2021
Notch fracture toughness of glasses: Rate, age and geometry dependence text January 2016
Notch Fracture Toughness of Glasses: Dependence on Rate, Age, and Geometry journal August 2016
Coarse graining atomistic simulations of plastically deforming amorphous solids journal May 2017

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
Chorin-type projection method
Elastoplasticity
Fluid mechanics
Plasticity