Fundamental formulation for anti-plane eigenstrain problems

In this paper, the anti-plane eigenstrain problems are addressed in the framework of plane strain. A fundamental solution for an anti-plane eigenstrain nucleus located in an infinite plane is derived first. With this solution, the anti-plane eigenstrain toughening problems are formulated by Green's function method, which includes plastic strain shielding problems and transformation toughening problems. Also, with the equivalent eigenstrain principle and the Green's function method, its application to formulating inhomogeneous inclusion problems subjected to anti-plane load is demonstrated. The fundamental formulations and the related examples introduced here may pave a way to explore more complex problems in the corresponding aspects.