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In the quasistatic case, the “Eshelby principle for an interface”, namely, that the total, including the external loading, “driving force” (energy-momentum tensor) must vanish on the boundary, so that it can move incrementally with associated generation of eigenstrain, is demonstrated explicitly for a half-space plane boundary under dilatational eigenstrain.

Driving forces on phase boundaries: “The Eshelby principle for an interface”