权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Approaches to Fracture Mechanics based on Local and Global Energy Minimization

基于局部和全局能量最小化的断裂力学方法

基本信息

批准号：
34281900
负责人：
Professor Dr.-Ing. Christian Miehe (†)
金额：
--
依托单位：
Lehrstuhl für Materialtheorie
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2007
资助国家：
德国
起止时间：
2006-12-31 至 2012-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/34281900?language=en
关键词：
Approaches Fracture Mechanics based Local

项目摘要

The energetic framework of brittle fracture proposed by Griffith is unable to predict crack initiation in a body free of defects. This problem can be overcome by a global minimization of suitably defined incremental energy functionals having both volume and surface contributions. Problems governed by such functionals involving volume and surface energies appear in a variety of areas in applied sciences, ranging from image and signal processing to fracture mechanics. In order to deal numerically with these kind of problems, many approximate functional representations have been proposed, using high-order singular perturbations, finite differences or non-local energies. However, comprehensive theoretical treatments of incremental minimization methods for fracture in an engineering language and their associated computational implementations suitable for large-scale engineering applications are missing in the literature. The purpose of the project is to investigate theoretical and computational frameworks of brittle and cohesive fracture based on global energy minimization that a priori circumvent the main drawback of Griffith’s theory with regard to crack initiation. In the first period of the research project the following results have been obtained: Local energy minimization concepts of fracture based on configurational–force–driven sharp crack propagation were extended to the three–dimensional setting. Results obtained from this work provide reference solutions for the subsequent developments on global methods. Global energy minimization concepts were developed for a diffusive crack propagation, were a set of regularized crack discontinuities is described by a phase field which is driven by a gradient–type balance equation. The proposed framework results in a smooth continuum–damage–type theory of fracture with specific constitutive functions. An extended three–field model that consists of the displacement field, the fracture phase field and the dual dissipative force field was developed, whose viscous over–force structure provides a very robust computational setting of diffusive crack propagation with an enormous potential with regard to the modeling of complex three–dimensional crack topologies. In the subsequent period of the research project, we will improve the phase field model of fracture with regard to the modeling of more complex crack topologies as well as its extension to multi–field environments. As it turned out in the first research period, a very important aspect is its embedding into adaptive mesh refinement procedures which resolve diffusive crack zones. To this end, new configurational–force–driven mesh refinement indicators will be developed for the gradient–type phase field model of fracture. Furthermore, we plan to investigate problems of dynamic fracture including complex crack branching. Finally, we will underline the advantage of bulk constitutive modeling inherent in the phase field modeling of fracture with regard to its embedding into more complex multi–field problems such as coupled thermo–mechanical and electro–magneto–mechanical problems.

Griffith提出的脆性断裂的能量框架不能预测没有缺陷的物体中的裂纹萌生。这个问题可以通过适当定义的增量能量泛函的体积和表面贡献的全局最小化来克服。由这样的泛函涉及体积和表面能的问题出现在各种领域的应用科学，从图像和信号处理断裂力学。为了处理这类问题的数值计算，已经提出了许多近似的功能表示，使用高阶奇异摄动，有限差分或非局部能量。然而，增量最小化方法断裂的工程语言和其相关的计算实现适合于大规模的工程应用的综合理论治疗在文献中缺失。该项目的目的是研究基于全局能量最小化的脆性和内聚断裂的理论和计算框架，该框架先验地规避了Griffith理论在裂纹萌生方面的主要缺陷。在研究项目的第一阶段，取得了以下成果：局部能量最小化断裂的概念的基础上的配置力驱动的尖锐裂纹扩展到三维设置。从这项工作中获得的结果提供了参考解决方案的后续发展的全球方法。针对扩散裂纹扩展问题提出了全局能量最小化概念，其中一组正则化裂纹不连续性由梯度型平衡方程驱动的相场描述。建议的框架结果在一个光滑的连续损伤型断裂理论与特定的本构函数。一个扩展的三场模型，包括位移场，断裂相场和双耗散力场的开发，其粘性过力结构提供了一个非常强大的计算设置的扩散裂纹扩展方面的建模复杂的三维裂纹拓扑结构的巨大潜力。在研究项目的后续阶段，我们将改进相场模型的断裂方面的建模更复杂的裂纹拓扑结构，以及其扩展到多场环境。在第一个研究阶段，一个非常重要的方面是它嵌入到自适应网格细化程序，解决扩散裂纹区。为此，将为裂缝的梯度型相场模型开发新的构型力驱动的网格细化指标。此外，我们计划调查问题的动态断裂，包括复杂的裂纹分支。最后，我们将强调体本构建模固有的相场建模断裂方面的嵌入到更复杂的多领域的问题，如耦合的热-机械和电磁-机械问题的优势。