Dissipation potentials from elastic collapse. (28th June 2019)

• Record Type: Journal Article
• Authors: Goddard, Joe; Kamrin, Ken
• Is Part Of: Proceedings. Volume 475:Number 2226(2019)
• Publication Date: 2019-06-28
• Subjects: dissipative systems -- nonlinear Onsager symmetry -- elastic failure -- energy landscape; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2019.0144
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : 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 Körper. 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.