Generalization of Eshelby's formula for a single ellipsoidal elastic inclusion to poroelasticity and thermoelasticity

Eshelby's formula gives the response of a single ellipsoidal elastic inclusion in an elastic whole space to a uniform strain imposed at infinity. Using a linear combination of results from two simple thought experiments, we show how this formula may be generalized to both poroelasticity and thermoelasticity. The resulting new formulas are important for applications to analysis of poroelastic and thermoelastic composites, including but not restricted to rocks.