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Numerical implementation of a crystal plasticity model with dislocation transport for high strain rate applications

机译：高应变率应用中具有位错传输的晶体塑性模型的数值实现

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This paper details a numerical implementation of a single crystal plasticity model with dislocation transport for high strain rate applications. Our primary motivation for developing the model is to study the influence of dislocation transport and conservation on the mesoscale response of metallic crystals under extreme thermo-mechanical loading conditions (e.g. shocks). To this end we have developed a single crystal plasticity theory (Luscher et al (2015)) that incorporates finite deformation kinematics, internal stress fields caused by the presence of geometrically necessary dislocation gradients, advection equations to model dislocation density transport and conservation, and constitutive equations appropriate for shock loading (equation of state, drag-limited dislocation velocity, etc). In the following, we outline a coupled finite element-finite volume framework for implementing the model physics, and demonstrate its capabilities in simulating the response of a [1 0 0] copper single crystal during a plate impact test. Additionally, we explore the effect of varying certain model parameters (e.g. mesh density, finite volume update scheme) on the simulation results. Our results demonstrate that the model performs as intended and establishes a baseline of understanding that can be leveraged as we extend the model to incorporate additional and/or refined physics and move toward a multi-dimensional implementation.
机译：本文详细介绍了高应变速率应用中具有位错传输的单晶塑性模型的数值实现。我们开发该模型的主要动机是研究位错迁移和守恒对极端热机械载荷条件下（例如冲击）金属晶体的中尺度响应的影响。为此，我们开发了一种单晶可塑性理论（Luscher等人（2015）），该理论结合了有限变形运动学，由于存在几何上必要的位错梯度而引起的内部应力场，对位错密度传输和守恒进行建模的对流方程以及本构关系。适用于冲击载荷的方程（状态方程，受阻力限制的位错速度等）。在下文中，我们概述了用于实现模型物理的耦合有限元-有限体积框架，并展示了其在板冲击试验中模拟[1 0 0]铜单晶响应的能力。此外，我们探讨了更改某些模型参数（例如网格密度，有限体积更新方案）对模拟结果的影响。我们的结果表明，该模型能够按预期执行，并建立了理解的基线，随着我们扩展该模型以纳入其他和/或改进的物理方法，并朝着多维实现的方向发展，可以利用该基线。

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