On the inviscid limit of a model for crack propagation
On the inviscid limit of a model for crack propagation
复制标题
裂纹扩展模型的无粘极限
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
C. Zanini
中科院分区：
文献类型：
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作者：
D. Knees;A. Mielke;C. Zanini
我们研究了弹性体中单个裂纹的演化，并假设裂纹路径是事先已知的。基于Griffith的局部能量释放率准则，将裂纹尖端的运动模拟为与速率无关的过程。根据该准则，系统在执行跳跃之前可以停留在局部最小值。本文的目标是证明存在这样的演变，并阐明了当地的能量释放率标准和模型的基础上的全球稳定性标准（例如Francfort/Marigo模型）之间的差异。我们通过消失粘性方法构造局部模型的解，并比较弱解、局部解和全局解的不同概念。
We study the evolution of a single crack in an elastic body and assume that the crack path is known in advance. The motion of the crack tip is modeled as a rate-independent process on the basis of Griffith’s local energy release rate criterion. According to this criterion, the system may stay in a local minimum before it performs a jump. The goal of this paper is to prove existence of such an evolution and to shed light on the discrepancy between the local energy release rate criterion and models which are based on a global stability criterion (as for example the Francfort/Marigo model). We construct solutions to the local model via the vanishing viscosity method and compare different notions of weak, local and global solutions.