Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 300, Issue -, Pages 136-166Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2015.06.046
Keywords
Fluid mechanics; Chorin-type projection method; Plasticity; Elastoplasticity
Funding
- National Science Foundation [DMR-1409560]
- Office of Science, Computational and Technology Research, U.S. Department of Energy [DE-AC02-05CH11231]
- Minerva Foundation
- Federal German Ministry for Education and Research
- Israel Science Foundation [712/12]
- Harold Perlman Family Foundation
- William Z. and Eda Bess Novick Young Scientist Fund
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1408685] Funding Source: National Science Foundation
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1409560] Funding Source: National Science Foundation
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A well-established numerical approach to solve the Navier-Stokes equations for incompressible fluids is Chorin's projection method [1], 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. 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. (C) 2015 Elsevier Inc. All rights reserved.
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