On the microlocal modelling of thermoelastic periodic composites

Stanislaw J. Matysiak (1) , Czeslaw Wozniak (1)

1 UW - University of Warsaw

In the recent formulations of various homogenized models for periodic material structures two main lines of modelling can be distinguished. The first line is based on rather intuitive physical assumptions and lead to various engineering theories of composite materials. An excelent example of this approach is given in a book by R. JONES [4], where also a list of references can be found. The second line of approach takes into account some asymptotic theorems of analysis and is resumed in books by A. BENSOUSSAN, J. L. LIONS, G. PAPANICOLAOU [2], E. SANCHEZ-PALENCIA [16] or N. S. BAHVALOV, G. P. PANASENKO [1]. A certain alternative approach to the modelling of periodic composites has been proposed lately in [19, 21, 23 ,24 - 26, 28, 29], where the concepts of the nonstandard analysis combined with some postulated a priori heuristic assumptions resulted in new homogenized models of the composites under consideration. These models, in the case of thermoelastic periodic composites, are governed by systems of equations for unknown macrodeformations, macrotemperatures and for certain extra unknowns called microlocal parameters. The microlocal parameters (kinematicaL and thermal) make it possible to evaluate not only mean but also local values of defom1ation and temperature gradients and hence stresses and heat fluxes in every material component of the composite. That is why the homogenized models obtained in [19, 21, 23, 24 - 26, 28, 29] can be referred to as the models with microlocal parameters. The first aim of the paper is to discuss the general form of the homogenized models with microlocal parameters for the thermoelastic periodic composites and then to pass to the linearized form of equations. After that various applications of the derived equations as well as some special problems are analysed.

Domaines: Mécanique [physics.med-ph]

Stanislaw J. Matysiak, Czeslaw Wozniak. On the microlocal modelling of thermoelastic periodic composites. 2014. ⟨hal-00944510⟩