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1982). , Academic Press, New York. Malvern, L. E. (1969). Introduction to the Mechanics of Continuous Medium, Prentice-Hall, Englewood Cliffs, NJ. Ting, T. C. T. (1996). Anisotropic Elasticity—Theory and Applications, Oxford University Press, New York. 48 BASIC EQUATIONS OF CONTINUUM MECHANICS SUGGESTED READINGS Fung, Y. C. (1965). Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, NJ. Mura, T. (1987). Micromechanics of Defects in Solids, Martinus Nijhoff, Dordrecht. 3 EIGENSTRAINS In this chapter, we will ﬁrst deﬁne what eigenstrain is and give some examples of it.

38) Under constant strain kj(t) ϭ kj(0), we have dkl(t)/dt ϭ 0. 37) reduces to ij(t) ϭ Gijkl(t)kj(0). 39) This is the reason that Gijkl(t) is termed a relaxation function, for it represents the stress relaxation under constant strain. 40) where it has been assumed that for t Ͻ 0, both ij(t) and Jijkl(t) are zero, that is, ij(t) ϭ 0 and Jijkl(t) ϭ 0 for t Ͻ 0. The fourth-order tensor function Jijkl(t) is called the creep function because under constant stress kj(t) ϭ kj(0), we have dkl(t)/dt ϭ 0.

When both elastic strain and eigenstrain coexist in a continuum, the total strain is given by the sum Fundamentals of Micromechanics of Solids. Jianmin Qu and Mohammed Cherkaoui © 2006 John Wiley & Sons, Inc. ISBN: 978-0-471-46451-8 49 50 EIGENSTRAINS ij ϭ eij ϩ ij*. 1) The above equation implies that both the elastic strain and eigenstrain act together to cause a material point in the continuum to displace from its initial location to its ﬁnal location in the deformed conﬁguration. 2) where ui is the total displacement ﬁeld cause by both the elastic strain and the eigenstrain.