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首页> 外文期刊>International Journal of Solids and Structures >On large-strain finite element solutions of higher-order gradient crystal plasticity
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On large-strain finite element solutions of higher-order gradient crystal plasticity

机译：高阶梯度晶体可塑性的大应变有限元解

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摘要

A finite-strain higher-order gradient crystal plasticity model accounting for the backstress effect originating from the existence of geometrically necessary dislocations (GNDs) is applied to plane strain finite element analysis. Different element types are tested to seek out an element formulation that is reliable and useful for solving problems involving severe plastic deformation. In the present finite element formulation, the GND density rates are chosen to be additional nodal degrees of freedom. Different orders of shape functions are employed for the interpolation of displacement rates and GND density rates. Their effects on solutions are examined in detail by considering three boundary value problems: a simple shear of a constrained layer (a film), a compression problem with loading surfaces impenetrable to dislocations, and a tension problem involving shear band formation. In all the cases, the formulation in which eight-node elements with reduced integration and four-node elements with full integration are used respectively for displacement rates and the GND density rates gives reasonable solutions. In addition to the discussion on the choice of finite elements, detailed behavior in gradient-dependent solids, such as the accumulation of GND density and the distribution of backstress on each slip system, is investigated by utilizing the reliable computational results obtained.
机译：考虑平面应力有限元分析的有限应变高阶梯度晶体塑性模型，该模型考虑了因几何必要位错（GNDs）的存在而产生的背应力效应。测试了不同的元素类型，以找出可靠且有用的元素配方，以解决涉及严重塑性变形的问题。在当前的有限元公式中，将GND密度比率选择为额外的节点自由度。插值位移速率和GND密度速率采用了不同阶的形状函数。通过考虑三个边界值问题来详细检查它们对解决方案的影响：约束层（薄膜）的简单剪切，具有无法位错的加载表面的压缩问题以及涉及剪切带形成的拉伸问题。在所有情况下，将降低集成度的八节点元件和完全集成度的四节点元件分别用于位移速率和GND密度速率的公式给出了合理的解决方案。除了讨论有限元的选择外，还利用获得的可靠计算结果研究了梯度依赖型实体中的详细行为，例如GND密度的累积和每个滑移系统上的反应力分布。

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