Multipole expansion of continuum dislocations dynamics in terms of alignment tensors
Multipole expansion of continuum dislocations dynamics in terms of alignment tensors
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DOI：
10.1080/14786435.2015.1026297
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发表时间：
2014-09
影响因子：
1.6
通讯作者：
T. Hochrainer
中科院分区：
文献类型：
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作者：
T. Hochrainer
基于位错的塑性连续理论的发展仍然是应用物理和材料科学的核心挑战之一。发展位错的连续理论需要解决两个长期存在的问题：（i）找到一个合理数量的变量的位错运动学的忠实表示和（ii）根据这些变量导出位错动力学的平均描述（即材料定律）。在本文中，我们解决了第一个问题，即我们制定张量守恒律的分布有向线。这是通过在所谓的排列张量方面的位错密度的多极扩展来实现的，所述排列张量包含关于位错密度和位错曲率的方向分布的信息。由高维位错密度理论导出了这些张量的演化方程。低阶封闭近似这个层次导致连续位错塑性动力学模型，只有很少的内部变量。展望更精细的理论和当前的挑战，位错密度建模进行了讨论。
The development of a dislocation-based continuum theory of plasticity remains one of the central challenges of applied physics and materials science. Developing a continuum theory of dislocations requires the solution of two long-standing problems: (i) to find a faithful representation of dislocation kinematics with a reasonable number of variables and (ii) to derive averaged descriptions of the dislocation dynamics (i.e. material laws) in terms of these variables. In the current paper, we solve the first problem, i.e. we develop tensorial conservation laws for distributions of oriented lines. This is achieved through a multipole expansion of the dislocation density in terms of so-called alignment tensors containing information on the directional distribution of dislocation density and dislocation curvature. A hierarchy of evolution equations of these tensors is derived from a higher dimensional dislocation density theory. Low-order closure approximations of this hierarchy lead to continuum dislocation dynamics models of plasticity with only few internal variables. Perspectives for more refined theories and current challenges in dislocation density modelling are discussed.