Dissipation potentials from elastic collapse.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES(2019)
摘要
Generalizing Maxwell's (Maxwell 1867 IV. Phil. Trans. R. Soc. Lond. 157, 49-88 (doi: 10.1098/rstl.1867.0004)) classical formula, this paper shows how the dissipation potentials for a dissipative system can be derived from the elastic potential of an elastic system undergoing continual failure and recovery. Hence, stored elastic energy gives way to dissipated elastic energy. This continuum-level response is attributed broadly to dissipative microscopic transitions over a multi-well potential energy landscape of a type studied in several previous works, dating from Prandtl's (Prandtl 1928 Ein Gedankenmodell zur kinetischen Theorie der festen Korper. ZAMM 8, 85-106) model of plasticity. Such transitions are assumed to take place on a characteristic time scale T, with a nonlinear viscous response that becomes a plastic response for T -> 0. We consider both discrete mechanical systems and their continuum mechanical analogues, showing how the Reiner-Rivlin fluid arises from nonlinear isotropic elasticity. A brief discussion is given in the conclusions of the possible extensions to other dissipative processes.
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关键词
dissipative systems,nonlinear Onsager symmetry,elastic failure,energy landscape
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