论文标题
正式层次结构有多有用？关于平均脱位动力学以定义中摩克罗可塑性的案例研究
How useful are formal hierarchies? A case study on averaging dislocation dynamics to define meso-macro plasticity
论文作者
论文摘要
精确演化方程的形式层次结构是针对微观脱位动力学状态函数的物理相关时空平均值得出的。尽管这样的层次结构无疑具有某种价值，但这里的主要目标是揭示此类非线性偏微分方程系统的棘手的复杂性，这些方程仍然“非关闭”，因此要遵守现象学假设。取而代之的是，建议在最早的阶段终止此类层次结构，并花费努力来得出闭合关系，以考虑到正式平均术语所产生的“非关闭”术语，这是通过考虑到全部压力耦合的微观脱位动力学的正式平均术语，无论是在哪种正式的等级方面，无论是在哪种正式的等级方面，无论是动力学理论类型还是在这里使用，还是无声的。
A formal hierarchy of exact evolution equations are derived for physically relevant space-time averages of state functions of microscopic dislocation dynamics. While such hierarchies are undoubtedly of some value, a primary goal here is to expose the intractable complexity of such systems of nonlinear partial differential equations that, furthermore, remain `non-closed' and therefore subject to phenomenological assumptions to be useful. It is instead suggested that such hierarchies be terminated at the earliest stage possible and effort be expended to derive closure relations for the `non-closed' terms that arise from the formal averaging by taking into account the full-stress-coupled microscopic dislocation dynamics, a matter on which these formal hierarchies, whether of kinetic theory type or as pursued here, are silent.
