An Eulerian projection method for quasi-static elastoplasticity

被引:18
作者
Rycroft, Chris H. [1 ,2 ]
Sui, Yi [3 ]
Bouchbinder, Eran [4 ]
机构
[1] Harvard Univ, Paulson Sch Engn & Appl Sci, Cambridge, MA 02138 USA
[2] Univ Calif Berkeley, Lawrence Berkeley Natl Lab, Dept Math, Berkeley, CA 94720 USA
[3] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada
[4] Weizmann Inst Sci, Dept Chem Phys, IL-76100 Rehovot, Israel
基金
美国国家科学基金会; 以色列科学基金会;
关键词
Fluid mechanics; Chorin-type projection method; Plasticity; Elastoplasticity; NAVIER-STOKES EQUATIONS; ELASTIC-PLASTIC SOLIDS; MACH NUMBER COMBUSTION; METALLIC GLASSES; NUMERICAL-SOLUTION; INHOMOGENEOUS DEFORMATION; STRESS; FORMULATION; ALGORITHMS; SIMULATION;
D O I
10.1016/j.jcp.2015.06.046
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
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.
引用
收藏
页码:136 / 166
页数:31
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