Abstract Hypo-elastoplasticity is a flexible framework for modeling the mechanics of many hard materials under small elastic deformation and large plastic deformation. Under typical loading rates, most laboratory tests of these materials happen in the quasi-static limit, but there are few existing numerical methods tailor-made for this physical regime. In this work, we extend to three dimensions a recent projection method for simulating quasi-static hypo-elastoplastic materials. The method is based on a mathematical correspondence to the incompressible Navier–Stokes equations, where the projection method of Chorin (1968) is an established numerical technique. We develop and utilize a three-dimensional parallel geometric multigrid solver employed to solve a linear system for the quasi-static projection. Our method is tested through simulation of three-dimensional shear band nucleation and growth, a precursor to failure in many materials. As an example system, we employ a physical model of a bulk metallic glass based on the shear transformation zone theory, but the method can be applied to any elastoplasticity model. We consider several examples of three-dimensional shear banding, and examine shear band formation in physically realistic materials with heterogeneous initial conditions under both simple shear deformation and boundary conditions inspired by friction welding.

中文翻译：

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准静态弹塑性固体的平行三维模拟

摘要 低弹塑性是一种灵活的框架，用于模拟许多硬质材料在小弹性变形和大塑性变形下的力学。在典型的加载速率下，这些材料的大多数实验室测试都是在准静态极限下进行的，但很少有针对这种物理状态量身定制的现有数值方法。在这项工作中，我们将最近用于模拟准静态低弹塑性材料的投影方法扩展到三个维度。该方法基于与不可压缩 Navier-Stokes 方程的数学对应关系，其中 Chorin (1968) 的投影方法是一种成熟的数值技术。我们开发并利用了用于求解准静态投影的线性系统的三维平行几何多重网格求解器。我们的方法通过模拟三维剪切带成核和生长进行测试，这是许多材料失效的前兆。作为示例系统，我们采用基于剪切转变区理论的块状金属玻璃的物理模型，但该方法可应用于任何弹塑性模型。我们考虑了 3 维剪切带的几个示例，并在简单剪切变形和受摩擦焊接启发的边界条件下，研究了具有异质初始条件的物理现实材料中剪切带的形成。