Thermodynamic framework for variance-based non-local constitutive models

The present work deals with the development of a framework dedicated to construction constitutive models non-local internal variables. Such variables allow considering impact microstructural changes on current state material point. Non-locality is introduced by considering, not only spatial average, but also variance an variable in relations. proposed relies continuum thermodynamics construct set equations. allows including some information regarding distribution when constructing for thermomechanical applications. In contrast gradient-type models, this strategy does require additional equilibrium equations and boundary conditions. For purpose illustration, numerical examples are presented. According results, can be used circumvent difficulties associated excessive localization or consider size effects.