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Multiscale GFEM with superposition of crack enrichment functions driven by finite fracture mechanics: Theory, first computation and open problems

机译：由有限断裂力学驱动的具有裂纹扩展功能叠加的多尺度GFEM：理论，首次计算和开放问题

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This work presents a direct extension of the multiscale GFEM (MS-GFEM) where damage and fracture mechanisms are now taken into account. Using a pattern-based description of the microscale, the construction of the model falls into two main parts: the modeling of a multiphase composite yarn, and the modeling of crack events inside the microstructure. The classical difficulties associated with the implementation and computation cost of the GFEM are dealt through a multiscale approach based on the Saint-Venant principle. This multiscale vision enables the microstructure and the microldnematics to be handled on the scale of the pattern independently of the macroscale discretization. Additionally, numerical enrichment functions are superimposed between the existing enrichment functions in a local computational domain. These enrichment functions deliver accurate solutions of crack interactions among local features, like inclusions, voids, etc, and are specifically appealing to evolution type problems like the crack events defined under the finite fracture mechanics framework. Different crack patterns can be introduced at different positions in the global domain when certain fracture criteria are met. The multiscale approach is implemented inside the finite element software Cast3M in order to use the existing infrastructure of the object oriented code for the development of MS-GFEM. (C) 2016 Elsevier Ltd. All rights reserved.
机译：这项工作提出了多尺度GFEM（MS-GFEM）的直接扩展，其中现已考虑到破坏和断裂机制。使用基于模式的微观尺度描述，模型的构建分为两个主要部分：多相复合纱线的建模和微观结构内部裂缝事件的建模。与GFEM的实现和计算成本相关的经典难题是通过基于Saint-Venant原理的多尺度方法解决的。这种多尺度的视野使微观结构和微观特征与宏观尺度离散化无关地在图案的尺度上进行处理。另外，在局部计算域中，将数字富集函数叠加在现有的富集函数之间。这些富集功能提供了局部特征（如内含物，空隙等）之间的裂纹相互作用的精确解决方案，并且特别吸引了诸如有限断裂力学框架下定义的裂纹事件之类的演化类型问题。当满足某些断裂标准时，可以在全局域的不同位置引入不同的裂纹模式。多尺度方法是在有限元软件Cast3M内部实现的，以便使用面向对象代码的现有基础结构来开发MS-GFEM。 （C）2016 Elsevier Ltd.保留所有权利。

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