'Hypertractions and hyperstresses convey the same mechanical information Continuum Mech. Thermodyn. (2010) 22:163-176' by Prof. Podio Guidugli and Prof. Vianello and some related papers on higher gradient theories

dell'Isola, Francesco; Seppecher, Pierre
August 2011
Continuum Mechanics & Thermodynamics;Aug2011, Vol. 23 Issue 5, p473
Academic Journal
In this commentary, we try to make clearer the state of the art concerning the relation between mechanical contact interactions and the different notions of stresses. We emphasize the importance of the concept of virtual displacements. Its role has been recognized in Mechanics and in Continuum Mechanics long ago (see e.g., Vailati in Il principio dei lavori virtuali da Aristotele a Erone d'Alessandria, 113-128, ; Russo in The forgotten revolution, Springer, Berlin, , or Cosserat and Cosserat in Sur la Th�orie des Corps D�formables, Herman, Paris, ; Cosserat and Cosserat in Note sur la th�orie de l.action euclidienne, Gauthier-Villars, Paris, ), and it is central as well when starting with an expression of the power expended by internal stresses and deducing the form of contact interactions as when starting with some form of the contact interactions and developing a representation theorem for these contact interactions based on the Cauchy tetrahedron construction.


Related Articles

  • Polymer Networks with Slip-links: 1. Constitutive Equations for an Uncross-linked Network. Drozdov, A. // Continuum Mechanics & Thermodynamics;Sep2006, Vol. 18 Issue 3/4, p157 

    Constitutive equations are derived for the mechanical response of polymers at three-dimensional deformations with finite strains. A polymer is treated as an incompressible network of flexible chains with free ends whose motion at the micro-level is constrained by a random number of slip-links....

  • Equations of the Dynamic Problem of Thermoelasticity in Stresses in a Three-Orthogonal Coordinate System. Musii, R.; Stasyuk, H. // Materials Science;Jan2005, Vol. 41 Issue 1, p74 

    By using the system of source equations including the equations of motion, Cauchy relations, generalized Hooke’s law, and Saint-Venant compatibility equations for strains, we deduce the system of defining equations for the dynamic problem of thermoelasticity in stresses in an arbitrary...

  • Eshelby's formula for an ellipsoidal elastic inclusion in anisotropic poroelasticity and thermoelasticity. Levin, Valery M.; Alvarez-Tostado, Juan M. // International Journal of Fracture;Mar2003, Vol. 119 Issue 4, pL79 

    Eshelby's formula that relates the strain inside of an ellipsoidal inclusion in an unbounded elastic medium to the uniform strain imposed at infinity is generalized to the cases of poroelastic and thermoelastic materials. This result holds for an arbitrary anisotropy of the inclusion and of the...

  • On the consequences of the constraint of incompressibility with regard to a new class of constitutive relations for elastic bodies: small displacement gradient approximation. Bustamante, R.; Rajagopal, K. // Continuum Mechanics & Thermodynamics;Mar2016, Vol. 28 Issue 1/2, p293 

    Recently, there has been an interest in the development of implicit constitutive relations between the stress and the deformation gradient, to describe the response of elastic bodies as such constitutive relations are capable of describing physically observed phenomena, in which classical models...

  • Mixed variational principles in space and time for elastodynamics analysis. Quadrelli, M.B.; Atluri, S.N. // Acta Mechanica;1999, Vol. 136 Issue 3/4, p193 

    Nonlinear elastodynamics problems are approached from the point of view of a mixed variational principle. It is shown that four different functionals lead to different formulations of the problem with different independent fields. One of the functionals is specialized to the case of spatial...

  • Quasistatic Evolution Problems for Linearly Elastic�Perfectly Plastic Materials. Dal Maso, Gianni; DeSimone, Antonio; Mora, Maria Giovanna // Archive for Rational Mechanics & Analysis;May2006, Vol. 180 Issue 2, p237 

    The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded...

  • Theory of Elastic Dielectrics Revisited. Ericksen, J. L. // Archive for Rational Mechanics & Analysis;Feb2007, Vol. 183 Issue 2, p299 

    I develop a variational principle introduced in [2] for electromagnetic elastic bodies and discuss its consequences. Formulae for stress tensors and configurational stresses are derived by energy minimization.

  • Thermostressed state of a piezoelectric bodywith a plane crack under symmetric thermal load. Kirilyuk, V. // International Applied Mechanics;Mar2008, Vol. 44 Issue 3, p320 

    The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress (SIF) and electric displacement (EDIF) in...

  • Stress solutions to the three-dimensional problem of elasticity. Borodachev, N. // International Applied Mechanics;Aug2006, Vol. 42 Issue 8, p849 

    New representations of the stress tensor in the linear theory of elasticity and thermoelasticity are proposed. These representations satisfy the equilibrium equations and the strain compatibility equation. The stress tensor is expressed in terms of a harmonic tensor or a harmonic vector. The...


Read the Article


Sign out of this library

Other Topics