A PHENOMENOLOGICAL CONSTITUTIVE MODEL OF NON-CONVENTIONAL ELASTIC RESPONSE

作者：Panoskaltsis Vassilis P^*; Soldatos Dimitris

来源：International Journal of Applied Mechanics, 2013, 5(4).

DOI：10.1142/S1758825113500361

• Complex bodies
• spatial covariance of the balance of energy equation
• spatial diffeomorphism
• large deformations
• metric
• Doyle-Ericksen formula
• conservation and balance laws
• internal structure
• thermodynamics
• work done in a process
• hyperelasticity
• nonisothermal covariant constitutive theory

In this paper, a general model of elastic (non-dissipative) behavior is developed. This model belongs to a class of models, developed for the description of complex bodies, in which the local state is assumed to be determined not only by the deformation, but also by a family of additional material parameters. The latter, unlike some additional structures used in the mechanics of complex bodies (e.g., directors, order parameters, internal degrees of freedom), are not considered as interactions of microscopic nature; rather they are considered as variables of macroscopic nature that describe the internal structure of the material, while their rates describe the evolution of the internal structure in the course of deformation. Accordingly, these variables are assumed to evolve continuously with time in a manner that guaranties the reversibility of the applied dynamical process. A covariant theory for the continuum in question is derived by means of invariance properties of the global form of the spatial energy balance equation, under the superposition of arbitrary spatial diffeomorphisms. In particular, it is shown that the assumption of spatial covariance of the equation of balance of energy yields the standard conservation and balance laws of classical mechanics but it does not yield the standard Doyle-Ericksen formula. In fact, the "Doyle-Ericksen formula" derived in this work, has some extra terms in it, which are related directly to the internal structure of the material, as the latter is controlled by the additional parameters. In a similar manner, by assuming the absolute temperature as an additional state variable and by employing the invariance properties of the local form of the spatial balance of energy under superimposed spatial diffeomorphisms, which also include a temperature rescaling, a nonisothermal covariant constitutive theory is naturally obtained. A formal comparison of the proposed elastic material with the standard hyperelastic (Green elastic) solid is also presented.

• 出版日期2013-12