自适应韧性相场断裂的多级全局-局部技术
Multilevel Global-Local techniques for adaptive ductile phase-field fracture
摘要：
本文提出了一种基于严格变分的多层全局-局部韧性断裂理论。在这里，一个相场公式是用来解决故障机制，通过正规化的尖锐裂纹拓扑的局部状态。通过本构功密度函数实现了塑性与裂纹相场的耦合，本构功密度函数由退化的弹性储能和塑性与损伤的累积耗散能表征。基于乘性Schwarz交替法的思想，提出了两种不同的全局-局部方法：（1）首先提出了一个具有弹塑性行为的全局本构模型，然后用一个局部区域来描述弹塑性断裂响应。(ii)第二个模型的主要目标是引入一个采用全球本地的方法对多层次的本地设置。为此，一个弹塑性的整体本构模型增加了两个不同的局部域，其中，第一个局部域的行为作为一个弹塑性材料和下一个局部域建模由于断裂状态。为了进一步减少计算量，引入了全局-局部概念中的预测-校正自适应性。一个自适应计划的设计，通过有效的全球塑性流动的演变（只有弹塑性自适应），并通过局部裂纹相场状态的演变（只有断裂自适应）。因此，在计算过程中，两个局部区域被动态更新，从而产生双向自适应过程。使用单尺度问题验证了全局-局部方法在准确性/鲁棒性和效率方面的整体响应。由此产生的框架算法进行了详细描述，并与数值例子证实。
英文摘要：
This paper outlines a rigorous variational-based multilevel Global-Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state. The coupling of plasticity to the crack phase-field is realized by a constitutive work density function, which is characterized through a degraded stored elastic energy and the accumulated dissipated energy due to plasticity and damage. Two different Global-Local approaches based on the idea of multiplicative Schwarz' alternating method are proposed: (i) A global constitutive model with an elastic-plastic behavior is first proposed, while it is enhanced with a single local domain, which, in turn, describes an elastic-plastic fracturing response. (ii) The main objective of the second model is to introduce an adoption of the Global-Local approach toward the multilevel local setting. To this end, an elastic-plastic global constitutive model is augmented with two distinct local domains; in which, the first local domain behaves as an elastic-plastic material and the next local domain is modeled due to the fracture state. To further reduce the computational cost, predictor-corrector adaptivity within Global-Local concept is introduced. An adaptive scheme is devised through the evolution of the effective global plastic flow (for only elastic-plastic adaptivity), and through the evolution of the local crack phase-field state (for only fracture adaptivity). Thus, two local domains are dynamically updated during the computation, resulting with two-way adaptivity procedure. The overall response of the Global-Local approach in terms of accuracy/robustness and efficiency is verified using single-scale problems. The resulting framework is algorithmically described in detail and substantiated with numerical examples.
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