Eshelby Inclusion: Mechanics and Eigenstrains

This lecture covers the Eshelby method for mechanics of inclusions, focusing on particles undergoing shape changes due to eigenstrains. It explains the concept of eigenstrains, stresses, and energies inside inclusions, and the analytical solutions for ellipsoidal inclusions. The lecture also delves into the Voigt notation for Eshelby and the Fourth Order Identity tensor, providing insights into stress and strain fields, displacement fields, and equilibrium conditions. The instructor discusses the characteristics of the Eshelby tensor, the minor symmetries, and the analytical solutions for elastic ellipsoidal inclusions. The lecture concludes with the application of the Eshelby method to solve mechanics problems with red point forces.