An Eulerian projection method for quasi-static elastoplasticity

摘要: A well-established numerical approach to solve the Navier-Stokes equations for incompressible fluids is Chorin's projection method 1, whereby fluid velocity explicitly updated, and then an elliptic problem pressure solved, which used orthogonally project field maintain incompressibility constraint. In this paper, we develop a mathematical correspondence between Newtonian in limit hypo-elastoplastic solids slow, quasi-static limit. Using correspondence, formulate new fixed-grid, Eulerian simulating solids, stress quasi-staticity We finite-difference implementation of apply it elasto-viscoplastic model bulk metallic glass based on shear transformation zone theory. show that two-dimensional plane strain simple simulation, quantitative agreement with explicit method. Like method, efficient numerically robust, making practical wide variety applications. also demonstrate can be extended simulate objects evolving boundaries. highlight number correspondences mechanics elastoplasticity, creating possibilities translating other methods two classes physical problems.