Crack Tip Equation of Motion in Dynamic Gradient Damage Models

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• 作者：Tianyi Li ; Jean-Jacques Marigo
• 关键词：Dynamic fracture ; Gradient damage models ; Variational methods ; Shape derivative methods ; Griffith’s law
• 刊名：Journal of Elasticity
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：127
• 期：1
• 页码：25-57
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Classical Mechanics; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-2681
• 卷排序：127

文摘

We propose in this contribution to investigate the link between the dynamic gradient damage model and the classical Griffith’s theory of dynamic fracture during the crack propagation phase. To achieve this main objective, we first rigorously reformulate two-dimensional linear elastic dynamic fracture problems using variational methods and shape derivative techniques. The classical equation of motion governing a smoothly propagating crack tip follows by considering variations of a space-time action integral. We then give a variationally consistent framework of the dynamic gradient damage model. Owing to the analogies between the variational ingredients of these two models and under some basic assumptions concerning the damage band structuration, one obtains a generalized Griffith criterion which governs the crack tip evolution within the non-local damage model. Assuming further that the internal length is small compared to the dimension of the body, the previous criterion leads to the classical Griffith’s law through a separation of scales between the outer linear elastic domain and the inner damage process zone.