Modeling Fractional Order Strain in Dipolar Thermoelasticity

摘要

The theory of dipolar thermoelasticity or, equivalently, thermoelasticity with microstructure arises in the field of mechanics of generalized continua. This article proposes a new mathematical model by considering the strain with fractional order in this theory. Introducing the Caputo fractional derivative in the classical case leads to new constitutive equations and to a reciprocity relation. The results presented in this article could be used to better model materials with microstructure for which classical mechanics fails to give the same output as expected by experiments.