Classical results for a non-classical theory: remarks on thermodynamic relations in Green�Naghdi thermo-hyperelasticity

Bargmann, Swantje; Steinmann, Paul
June 2007
Continuum Mechanics & Thermodynamics;Jun2007, Vol. 19 Issue 1/2, p59
Academic Journal
In this contribution we first investigate the thermodynamic�s relation between the entropy flux H and the heat flux Q in the non-classical theory of Green and Naghdi imposed by the entropy equality used in their approach. We show that the classical assumption entropy flux = heat flux/absolute temperature holds for isotropic materials by exploiting the entropy principle of M�ller and Liu. As opposed to the usual procedure, we formulate the balance laws with respect to the material description. Subsequently, further restrictions are obtained by exploiting the entropy principle as suggested by Green and Naghdi (in Proc. R. Soc. Lond. 432, 171�194, 1991). This yields the classical potential relations between the entropy and the free energy and between the second Piola-Kirchhoff stress tensor and the free energy.


Related Articles

  • Modeling of the differential rotation effect in complex loading of granular media. Kraus, E. I.; Lavrikov, S. V.; Medvedev, A. E.; Revuzhenko, A. F.; Shabalin, I. I. // Journal of Applied Mechanics & Technical Physics;Jul2009, Vol. 50 Issue 4, p661 

    A plane problem of directed mass transfer in a granular medium, induced by complex loading with continuous rotation of the principal axes of the strain tensor, is considered. It is proposed to use a hypoplastic model of a granular medium and a model of similarity of a viscous incompressible...

  • Investigation of Heat Transfer Phenomena in a Ventilated Disk Brake Rotor with Straight Radial Rounded Vanes. Talati, F.; Jalalifar, S. // Journal of Applied Sciences;2008, Vol. 8 Issue 20, p3583 

    In this research, two major models are used for calculation of frictional heat generation: namely macroscopic and microscopic model. In the macroscopic model, the law of conservation of energy or First Law of Thermodynamics is taken into account. And for the microscopic model, parameters such as...

  • Definition of the Temperature and Heat Flux in Micromilling of Hardened Steel Using the Finite Element Method. Ribeiro Filho, Sergio; Gomes, Marcelo; Lauro, Carlos; Brandão, Lincoln // Arabian Journal for Science & Engineering (Springer Science & Bu;Oct2014, Vol. 39 Issue 10, p7229 

    This paper shows the influence of the mesh size on the heat flux in the micromilling process. The definition of the heat flux was based on the inverse heat conduction method (IHCM), applying the finite element technique with the Eulerian-Lagrangian approach. The micromilling was simulated with a...

  • Volume-weighted mixture theory for granular materials. Chen, Kuo-Ching; Tai, Yih-Chin // Continuum Mechanics & Thermodynamics;Feb2008, Vol. 19 Issue 7, p457 

    In the present work we treat granular materials as mixtures composed of a solid and a surrounding void continuum, proposing then a continuum thermodynamic theory for it. In contrast to the common mass-weighted balance equations of mass, momentum, energy and entropy for mixtures, the...

  • Generating ensembles and measuring mixing in a model granular system. Puckett, James G.; Lechenault, Frédéric; Daniels, Karen E. // AIP Conference Proceedings;7/1/2009, Vol. 1145 Issue 1, p675 

    A major open question in the field of granular materials is the identification of relevant state variables which can predict macroscopic behavior. We experimentally investigate the mixing properties of an idealized granular liquid in the vicinity of its jamming transition, through the generation...

  • Microcanonical Entropy of the Infinite-State PottsModel. Johansson, Jonas; Pistol, Mats-Erik // Physics Research International;2011, p1 

    In this investigation we show that the entropy of the two-dimensional infinite-state Potts model is linear in configurational energy in the thermodynamic limit. This is a direct consequence of the local convexity of the microcanonical entropy, associated with a finite system undergoing a...

  • Thermal performance of trench backfills used for frost protection of water service lines. Zhao, Jack Q; Rajani, Balvant B; Daigle, Lyne // Canadian Geotechnical Journal;Feb2001, Vol. 38 Issue 1, p161 

    This paper describes the thermal performance of different configurations of trenches using various trench geometries and backfill and insulation materials. A limited number of laboratory tests were conducted to confirm the thermal properties of the backfills reported in the literature. The frost...

  • Finite element analysis of localization and micro�macro structure relation in granular materials. Part II: Implementation and simulations. Arslan, Haydar; Sture, S. // Acta Mechanica;May2008, Vol. 197 Issue 3/4, p153 

    The formation of strain localization influences the stability and stiffness of the soil mass or geosystem. The thickness of shear bands provides insight about overall strength and stiffness inside the granular body, and the shear band angle gives information about the failure surface in a given...

  • Design Formulas for the Groups of Six Cylindrical Silos Due to Interstice Loadings. Yuksel, S. Bahadir // Advances in Structural Engineering;Apr2011, Vol. 14 Issue 2, p265 

    Different and huge amounts of granular materials can be stored in and between the cells of the grouped reinforced concrete cylindrical silos. The determination of design forces acting on these grouped silos requires significant computational effort due to structural continuity and the force...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics