Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century by Gérard A. Maugin

Author:Gérard A. Maugin
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

7.1 Introduction

As its combined name indicates, visco-elasticity is a mechanical behaviour that combines elasticity and viscosity, most often in a linear manner. The following observable facts characterize this behaviour. Two typical related phenomena are creep and relaxation . The first of these corresponds to an increase of strain in time when stress is held constant, while relaxation is evidenced by a decrease of stress with time when the strain is held constant. Various models render these phenomena more or less correctly (cf. Finley et al. 1976). Moreover, when a cyclic loading is applied a hysteresis manifested by a phase lag is produced. This is related to a dissipation of mechanical energy. A direct consequence of the presence of viscosity, although often small in solids, is the attenuation of acoustic waves that propagate through a visco-elastic material. Visco-elastic materials abound and, in principle, all elastic materials can be made to exhibit the effects of a viscosity in particular if we wait long enough, centuries or millenaries—for glassware produced in antique times—so that Heraclitus’ old but spot on motto “ta panta rhei” (translated as “everything flows”) holds true. But actual examples of visco-elastic materials include some polymers, metals at high temperature, natural bio-materials (soft tissues), and bitumen materials. The range of strains is not necessarily limited to infinitesimal ones, as can be imagined with polymers and bio-materials. The scientific and technical interest in these materials has evolved in time.

Of course a mathematical description of visco-elasticity could not be envisaged before a sufficiency clear understanding of both elasticity and viscosity, hence before the middle of the nineteenth century. A development period in the corresponding modelling extends from the mid nineteenth century to the Second World War (see Sect. 7.2). It needed a firm connection with thermodynamics, but this had to await an accepted thermo-mechanical format (see Sect. 7.3). With the tremendous advances in theoretical rheology and rational continuum mechanics by scientists such as Oldroyd, Green and Rivlin, Truesdell, Coleman and Noll, Gurtin, Sternberg and others, visco-elasticity took a more strictly mathematical form—but substantiated by corresponding experiments in rheology —along with enlightening mathematical results (Sect. 7.5) and the introduction of an efficient description by means of internal variables of state (that typically characterize dissipative effects). This largely improved on old “hereditary” formulations (Boltzmann, Volterra, etc.) after a period of interest in establishing fundamental properties and problem solving by pioneers such as Lee, Mandel, Bland, Ilyushin, etc. (Sect. 7.4). The present contribution is not an abridged course on visco-elasticity (for which there exist many books, while regular graduate courses are delivered in so many places over the World). It rather purports at exposing the way various theories evolved in the self-evolving general background of continuum mechanics over a period of some hundred and fifty years. The approach is historical, with technicalities kept to a minimum.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.