The non-local generalized standard approach: a consistent gradient theory

Quoc Son Nguyen (1) , Stephane Andrieux (2)

1 LMS - Laboratoire de mécanique des solides
2 LAMSID - UMR 8193 - Laboratoire de Mécanique des Structures Industrielles Durables

In this paper, the generalized standard approach is proposed as a consistent gradient theory to include the gradients of the temperature and of the internal parameter in the set of state variables. This theory is derived from a global point of vue developping the basic ideas of continuum thermodynamics. It leads to the appropriate expressions of the entropy and of the internal energy in terms of the free energy in the case of temperature gradient. The local governing equations of the proposed thermodynamical approach are derived. The formalism of the dissipation potential can be applied in the same spirit as in the classical description from the dissipation analysis.

Mots clés: continuum thermodynamics; state variables; temperature gradient; internal parameter gragient; non-local generalized standard model

Domaines: Matériaux et structures en mécanique [physics.class-ph]

Quoc Son Nguyen, Stephane Andrieux. The non-local generalized standard approach: a consistent gradient theory. Comptes Rendus Mécanique, 2005, 333, pp.139-145. ⟨10.1016/j.crme.2004.09.010⟩. ⟨hal-00105139⟩