A Saint-Venant principle for shear band localization

被引：2
|
作者：
Horgan, CO [1 ]
Olmstead, WE
机构：
[1] Univ Virginia, Dept Civil Engn, Charlottesville, VA 22904 USA
[2] Northwestern Univ, Dept Engn Sci & Appl Math, Evanston, IL 60208 USA
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2003年 / 54卷 / 05期
关键词：
shear band localization; spatial decay of temperature; second-order nonlinear parabolic partial differential equations;
D O I：
10.1007/s00033-003-3202-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A type of Saint-Venant principle is derived for a two-dimensional model of shear band formation in thermoviscoplastic solids. To establish that the thermal energy generated during the formation process remains highly localized, a spatially decaying upper bound on the temperature is derived. It is found that the temperature bound decays exponentially along the direction perpendicular to the band, with a rate that decreases in time. The result is established by using maximum principles for second-order nonlinear parabolic partial differential equations.
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页码：807 / 814
页数：8
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