Two ways to estimate precipitate elastic fields through Eshelby inclusion theory

The stress-free misfit strain obtained from simulation, neglecting the constraint from the matrix phase, serves as the inhomogeneity eigenstrain. On the other hand, the experimentally measured misfit strain under the constraint of the matrix phase serves as the constrained strain. This study demonstrates two ways to calculate the equivalent eigenstrain for precipitates through Eshelby inclusion theory: the inhomogeneity eigenstrain way (IEW) and the constrained strain way (CSW).