Eigenstrain

The term was coined in the 1970s by Toshio Mura, who worked extensively on generalizing their mathematical treatment.

[2] Many distinct physical causes for eigenstrains exist, such as crystallographic defects, thermal expansion, the inclusion of additional phases in a material, and previous plastic strains.

[3] All of these result from internal material characteristics, not from the application of an external mechanical load.

Eigenstrain analysis usually relies on the assumption of linear elasticity, such that different contributions to the total strain

by Hooke’s Law:[3] In this form, the eigenstrain is not in the equation for stress, hence the term "stress-free strain".

(and thus, the total stress and strain fields) can only be found for specific geometries of the distribution of

[5] One of the earliest examples providing such a closed-form solution analyzed a ellipsoidal inclusion of material

Because the total strain, shown by the solid outlined ellipse, is the sum of the elastic and eigenstrains, it follows that in this example the elastic strain in the region

is the Eshelby Tensor, whose value for each component is determined only by the geometry of the ellipsoid.

The solution demonstrates that the total strain and stress state within the inclusion

In the general case, the resulting stresses and strains may be asymmetric, and due to the asymmetry of

Engineers can usually only acquire partial information about the eigenstrain distribution in a material.

[5] Understanding the total residual stress state, based on knowledge of the eigenstrains, informs the design process in many fields.

Residual stresses, e.g. introduced by manufacturing processes or by welding of structural members, reflect the eigenstrain state of the material.

In either case, the final stress state can affect the fatigue, wear, and corrosion behavior of structural components.

Since composite materials have large variations in the thermal and mechanical properties of their components, eigenstrains are particularly relevant to their study.

Local stresses and strains can cause decohesion between composite phases or cracking in the matrix.

These may be driven by changes in temperature, moisture content, piezoelectric effects, or phase transformations.

Particular solutions and approximations to the stress fields taking into account the periodic or statistical character of the composite material's eigenstrain have been developed.

[8] Controlling these strains can improve the electronic properties of an epitaxially grown semiconductor.