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.
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Mathematics Subject Classification (2000).
74C20, 74G50.
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Horgan, C., Olmstead, W. A Saint-Venant principle for shear band localization . Z. angew. Math. Phys. 54, 807–814 (2003). https://doi.org/10.1007/s00033-003-3202-5
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DOI: https://doi.org/10.1007/s00033-003-3202-5