Thermodynamics of the activated state of materials

The thermodynamics of irreversible processes is extended to deformable materials whose state and behavior under nonequilibrium conditions are determined by the value and evolution of the additional parameter — the activation parameter. General thermodynamic relations are presented. The concept of the time of existence of a nonequilibrium state is introduced, and the phase coexistence conditions are generalized taking into account the properties of the interface. Methods are described to generalize the relations for irreversible flows, thermodynamic forces, and the equations of state. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 141–152, January–February, 2009.     

Conewise linear elastic materials

Conewise linear elastic (CLE) materials are proposed as the proper generalization to two and three dimensions of one-dimensionalbimodular models. The basic elements of classical smooth elasticity are extended tononsmooth (or piecewise smooth) elasticity. Firstly, a necessary and sufficient condition for a stress-strain law to becontinous across the interface of the tension and compression subdomains is established. Secondly, a sufficient condition for the strain energy function to be strictlyconvex is derived. Thirdly, the representations of the energy function, stress-strain law and elasticity tensor are obtained fororthotropic, transverse isotropic andisotropic CLE materials. Finally, the previous results are specialized to apiecewise linear stress-strain law and it is found out that the pieces must be polyhedral convex cones, thus the CLE name.     

Thermodynamics and the potential energy of an elastic body

In this paper we consider an elastic body subject to conservative loads and immersed in an environment that is thermally passive and at constant temperature. We show that the potential energy in a configuration is greater than that in a configuration whenever the body reaches in a process from .

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Zusammenfassung In dieser Arbeit betrachten wir das Verhalten eines elastischen Körpers unter der Einwirkung konservativer äusserer Kräfte bei thermisch passiver und temperaturkonstanter Aussenwelt. Wir zeigen, dass die potentielle Energie in einer gegebenen Konfiguration grösser ist, als in jeder anderen durch einen Prozess von ihr aus erreichbaren Konfiguration.

     

Thermodynamical bounds to the elastic behaviour of elastic materials

We propose to exploit the second principle of thermodynamics in a different way from that usually followed in continuum mechanics. We study the consequences of this approach as far as the path-dependent character of the constitutive equations is concerned. The analysis leads us to infer that for materials capable of thermoelastic behaviour there are, in general, states of deformation beyond which a deformation process cannot occur without violating the second principle of thermodynamics. The relation between these states of deformation and those relevant to the yield limit is considered.     

Constraints in linearly elastic materials

The general theory of linear constraints in linear elasticity theory is outlined. For problems that are ill-posed in constraint theory although well-posed in the absence of any constraint, a modified form of constraint theory is proposed.

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Resume Les grandes lignes de la théorie générale des contraints en élasticité linéaire sont exposées. Une forme modifiée de la théorie des contraints est proposée pour les problèmes mal posés en présence de contraints quoique bien posés en l'absence de contraints.

     

Anisotropy of elastic properties of materials

Papers dealing with the generalized Hooke’s law for linearly elastic anisotropic media are reviewed. The papers considered are based on Kelvin’s approach disclosing the structure of the generalized Hooke’s law, which is determined by six eigenmoduli of elasticity and six orthogonal eigenstates. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 131–151, November–December, 2008.     

Antiplane deformations of inhomogeneous elastic materials

The system of equations governing antiplane deformations of inhomogeneous elastic media is examined with a view to achieving its reduction to a canonical form associated with the Cauchy-Riemann system.     

弹性拓扑材料研究进展

拓扑绝缘体起源于量子波动系统,因其单向传输、能量无耗散等新奇物理性质,近年逐渐被拓展到电磁波、声波、弹性波等经典波动领域,为经典波的调控提供了新思路.本文将系统介绍拓扑绝缘体理论及其在弹性波领域的相关研究进展.首先以一维、二维离散点阵系统为例,阐释拓扑物理研究中的基本数学、物理概念,如狄拉克锥、能带翻转、贝里曲率、拓扑...