Analytical aspects in strain gradient theory for chiral Cosserat thermoelastic materials within three Green-Naghdi models

Abstract

This work is motivated by the recent interest in using strain gradient theory to model the chiral behavior of elastic materials. In this paper, we derive a linear strain gradient theory for Cosserat thermoelastic materials according to the three models (types I, II and III) of Green-Naghdi theory. Models II and III permit propagation of thermal waves at finite speeds, while model I coincides with the classical Fourier’s law. The thermal field is influenced by the displacement and the microrotation fields and by some additional parameters that describe the chiral behavior. We prove the well-posedness for the three models and the asymptotic behavior for models I and III by the semigroup theory of linear operators.