A Saint-Venant principle for shear band
localization |
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| Authors: | C O Horgan W E Olmstead |
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| Institution: | (1) Department of Civil Engineering, University of Virginia, VA 22904 Charlottesville, USA;(2) Department of Engineering Sciences and Applied Mathematics, Northwestern University, IL 60208 Evanston, USA |
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| Abstract: | 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.Mathematics Subject Classification (2000). 74C20, 74G50. |
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| Keywords: | 74C20 74G50 |
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