An Eulerian projection method for quasi-static elastoplasticity

Rycroft, Chris H.; Sui, Yi; Bouchbinder, Eran

doi:10.1016/j.jcp.2015.06.046

Title: An Eulerian projection method for quasi-static elastoplasticity

Journal Article · 31 October 2015 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2015.06.046 · OSTI ID:1525116

Rycroft, Chris H. ^[1]; Sui, Yi ^[2]; Bouchbinder, Eran ^[3]

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
Simon Fraser Univ., Burnaby, BC (Canada). Dept. of Mathematics
Weizmann Inst. of Science, Rehovot (Israel). Chemical Physics Dept.

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.

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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

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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Notch fracture toughness of glasses: Rate, age and geometry dependence Vasoya, Manish; Rycroft, Chris H.; Bouchbinder, Eran arXiv https://doi.org/10.48550/arxiv.1604.02585	text	January 2016
Notch Fracture Toughness of Glasses: Dependence on Rate, Age, and Geometry Vasoya, Manish; Rycroft, Chris H.; Bouchbinder, Eran Physical Review Applied, Vol. 6, Issue 2 https://doi.org/10.1103/physrevapplied.6.024008	journal	August 2016
Coarse graining atomistic simulations of plastically deforming amorphous solids Hinkle, Adam R.; Rycroft, Chris H.; Shields, Michael D. Physical Review E, Vol. 95, Issue 5 https://doi.org/10.1103/physreve.95.053001	journal	May 2017

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Title: An Eulerian projection method for quasi-static elastoplasticity

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