Strain fields caused by doughnut-like and tubular inclusions with uniform eigenstrains

Inclusion problems for elongated toroidal inclusions are solved to discuss the strain fields caused by eigenstrained doughnut-like and tubular inclusions. For an infinitely long tubular inclusion, uniform eigenstrains do not generate elastic strains in the matrix region inside the tube. Effects of tube length on the elastic strains are shown for the purely dilatational eigenstrain ε*. For the tubular inclusion with the length 2b, the elastic strain at the center of the matrix region inside the tube becomes the maximum as much as ≈(a/b)ε* when the tubular inclusion has the inner diameter ≈2(b−a) and the outer diameter ≈2(b+a).