Some Notes on the Linear Viscoelasticity of Functional Graded Materials
Z.-H. Jin*
School of Areonautics and astronautics, Purdue University, West
Lafayette, IN 47907-1282, USA
* To whom correspondence should be addressed.
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Abstract |
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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 dilation 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 behaviour in
shear and dilation. 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.
Key Words:
Functionally graded material, viscoelasticity, correspondence principle, relaxation function, crack tip field, stress intensity factor
