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An eigenstrain is a local preferred deformation in the absence of stress. Constraints or incompatibility can make the actual strain differ from it, generating stress. Magnetostrictive strain is one example.

An eigenstrain is the deformation a material would prefer locally without applied stress. In a one-dimensional linear elasticity model, let $E$ be Young's modulus, take tension as positive stress, and write $\sigma =E(\epsilon -{\epsilon }^{\mathrm{mag}})$. A free rod has $\sigma =0$ and follows $\epsilon ={\epsilon }^{\mathrm{mag}}$. A perfectly blocked rod has $\epsilon =0$ and $\sigma =-E{\epsilon }^{\mathrm{mag}}$. Thus positive preferred elongation produces compressive stress when blocked.

For stipulated $E=100\mathrm{GPa}$, cross-sectional area $A=1\mathrm{m}{\mathrm{m}}^2$, and ${\epsilon }^{\mathrm{mag}}=20\times 10^{-6}$, blocking gives $\sigma =-2\mathrm{MPa}$ and axial force $F=\sigma A=-2\mathrm{N}$. This idealization ignores changes of magnetization caused by the load itself. A real magnetostrictive actuator therefore needs both magnetic and mechanical constitutive information: a free-length measurement alone does not determine its loaded motion.