Some Notes on the Linear Viscoelasticity of Functionally Graded Materials

Abstract

This work discusses the elastic-viscoelastic correspondence principle and the related issues in linear viscoelasticity of functionally graded materials (FGMs). It is clarified that the correspondence principle is directly applicable to certain boundary value problems of viscoelastic FGMs with closed-form solutions, and for general boundary value problems, the correspondence principle holds only for FGMs with variables separable relaxation moduli (moduli in separable form in space and time). For the relaxation moduli of an FGM to be variables separable, the time-dependence of the relaxation moduli in shear and dilatation should be identical. This imposes a rather severe restriction on the application of the correspondence principle to FGMs because engineering materials usually exhibit significantly different relaxation behavior in shear and dilatation. As an application of the correspondence principle, the stress and displacement fields near a stationary crack tip in a viscoelastic FGM are obtained. The paper also presents general stress intensity factor formulae for the crack problems of FGMs with separation of variables solutions.