An approximate 2-D solution for the shear-induced strain fields in eigenstrained cubic materials

An approximate analytical 2-D solution for the strain field components epsi lon (11), epsilon (12) and epsilon (22) occur ring in a cubic material due to a coherently bonded shear eigenstrained inclusion of cylindrical geometr y was obtained by means of Continuous Fourier Transforms (CFT). A Discrete Fourier Transform (DFT) based numerical model was used in order to test the validity of the results. For the case where the cylindrical inclusion and the surrounding media are elastically homogeneous and the orientation of th eir principal crystal axes are the samel a correlation between the analytic al and numerical models is demonstrated, both for strongly and weakly aniso tropic materials. Moreover, the strain fields within the inclusion are show n to be of homogeneous isotropic type. Finally, an expression for the close d-form strain energy of two cylindrical inclusions at arbitrary radius and angle was derived, and then used to determine the minimum energy configurat ion for the system.