A Saint-Venant principle for shear bandlocalization |
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| Authors: | C. O. Horgan W. E. Olmstead |
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| Affiliation: | (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 atwo-dimensional model of shear band formation inthermoviscoplastic solids. To establish that the thermal energygenerated during the formation process remains highly localized, aspatially decaying upper bound on the temperature isderived. It is found that the temperature bound decaysexponentially along the direction perpendicular to the band, witha rate that decreases in time. The result is established by usingmaximum principles for second-order nonlinear parabolic partialdifferential equations.Mathematics Subject Classification (2000). 74C20, 74G50. |
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| Keywords: | 74C20 74G50 |
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