https://hal-mines-paristech.archives-ouvertes.fr/hal-00542445Forest, SamuelSamuelForestMAT - Centre des Matériaux - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche ScientifiqueAifantis, EliasEliasAifantisUniversity of Thessaloniki - University of ThessalonikiSome links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continuaHAL CCSD2010Cattaneo equationGradient theoryMicromorphic theoryGradient plasticityHyperbolic heat equation[SPI.MAT] Engineering Sciences [physics]/MaterialsUMR7633, Bibliothèque2018-08-02 14:49:172022-10-22 05:10:122018-08-02 14:49:17enJournal articles10.1016/j.ijsolstr.2010.07.0091This work elaborates upon two robust models of gradient elasticity and gradient plasticity, and one gradient model of heat transfer, as originally advocated by the second author in the 1980's. The objective is, after recalling the links between these models and existing generalized continuum theories as developed in the 1960's and subsequently, to apply the same methodology to the case of diffusion with a view to establishing generalized transport equations. Aifantis double diffusivity and conductivity theory that provides generalized mass or heat transfer equations is compared to micromorphic-type hyper-temperature and micro-entropy proposals. The double temperature and the micromorphic thermal models are shown to lead to equations more general that Cattaneo's. The sign of the coefficient of the second time-derivative of temperature is found to differ according to both approaches. The double temperature model contains a fourth space derivative term not present in the micromorphic models. Such generalized equations can be useful, for example, in the interpretation of recent femtosecond laser experiments on metals.