Eigenstrain

The word "eigenstrain" has been introduced by T.Mura on the basis of the german words "Eigenspannungen" and "Eigenspannungsquellen".^[1] In the field of continuum mechanics, an eigenstrain is a kind of strain (deformation) produced without external forces (stress-free).^[2] Thermal expansion ^[3] and phase changes are eigenstrains. An eigenstrain can produce a self-equilibrated stress field called "eigenstress". As an example, if a piece of metal is not uniformly heated, the inhomogeneity of the thermal expansion (the incompatibility of the eigenstrain) induces stresses in the metal, without external forces: the eigenstress. A bimetal is used to estimate the temperature thanks to the deformation of the bimetal due to eigenstresses (here the temperature is uniform in the bimetal but not the eigenstrain, because of the difference of thermal expansion coefficients between the metals used in the bimetal). When a hot piece of glass is put under cold water, it can break because of this eigenstress.

References

1. Jun, T. S.; Korsunsky, A. M. (2010). "Evaluation of residual stresses and strains using the eigenstrain reconstruction method". International Journal of Solids and Structures. 47 (13): 1678–1686. doi:10.1016/j.ijsolstr.2010.03.002.
2. Mura, Toshio. Micromechanics of defects in solids. Vol. 3. Springer, 1987. http://link.springer.com/chapter/10.1007/978-94-009-3489-4_1
3. http://ciks.cbt.nist.gov/garbocz/manual/node9.html