Localization in inelastic rate dependent shearing deformations

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• 作者：Theodoros Katsaounis^a ; ^b ; ^{theodoros.katsaounis@kaust.edu.sa} ; Min-Gi Lee^a ; ^{mingi.lee@kaust.edu.sa} ; Athanasios Tzavaras^a ; ^c ; ^{athanasios.tzavaras@kaust.edu.sa}
• 关键词：Shear bands ; Hadamard instability ; Turing instability ; Shear localization ; Strain-rate sensitivity
• 刊名：Journal of the Mechanics and Physics of Solids
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：98
• 期：Complete
• 页码：106-125
• 全文大小：1106 K
• 卷排序：98

文摘

Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into an emerging coherent structure. We verify formation of shear bands for a nonlinear model exhibiting strain softening and strain rate sensitivity. The effects of strain softening and strain rate sensitivity are first assessed by linearized analysis, indicating that the combined effect leads to Turing instability. For the nonlinear model a class of self-similar solutions is constructed, that depicts a coherent localizing structure and the formation of a shear band. This solution is associated to a heteroclinic orbit of a dynamical system. The orbit is constructed numerically and yields explicit shear localizing solutions.