On the elastic axisymmetric deformation of a rod containing a single cylindrical inclusion

This paper studies the axisymmetric deformation of a rod containing a single cylindrical transformation inclusion with uniform axisymmetric eigenstrain. Elastic solutions of the problem are obtained by means of the principle of superposition. The original problem is divided into two sub-problems to derive the analytical expressions for the displacements, the stresses and the elastic strain energy of the whole rod. Quantitative pictures on the stress and strain jumps across the inclusion-matrix interface and on the evolution of the strain energy of the whole rod are illustrated. The results show that the normalized elastic strain energy depends on the relative length of the cylindrical inclusion for the length-radius ratio l/a < 2. This strain energy increases very quickly at the initial growth and soon reaches the peak value, then decreases with the further increase of l/a and finally reaches its steady state value. Several deformation features of this non-classical inclusion-matrix system are discussed. The work of this paper also provides a quantitative solution in the investigation of the propagation of strain discontinuity observed during thermoelastic phase transformation in solids such as TiNi shape memory alloy wires.