An approximate analytical 2D solution for the stresses and strains in eigenstrained cubic materials
Formal solutions for the Fourier transforms of stresses and strains in homogeneous but arbitrarily eigenstrained linearly elastic bodies are obtained with the help of continuous and discrete Fourier methods. The solutions are used to derive an analytical expression for the strains due to a dilatorically eigenstrained cylindrical inclusion in an infinite matrix, the inclusion and the matrix being made of cubic materials with the same orientation of principal axes. It is demonstrated with the help of discrete Fourier transform that the strains can be recovered by this solution, even for highly anisotropic materials. Further, continuous Fourier transform is used for the explicit computation of the total elastic energy due to dilatoric misfit of two differently sized cylinders in the cubic matrix. The expression for total elastic energy is written as a function of relative distance between cylinders as well as their orientation with respect to the main crystallographic axes. This expression is used to explain the formation of textures in cubic materials.
dilatorically eigenstrained cylindrical inclusion
scientific article; zbMATH DE number 1356550
scientific article