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

This paper studies the axisymmetric deformation of a rod containing a singl e cylindrical transformation inclusion with uniform axisymmetric eigenstrai n. 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 t he elastic strain energy of the whole rod. Quantitative pictures on the str ess and strain jumps across the inclusion-matrix interface and on the evolu tion of the strain energy of the whole rod are illustrated. The results sho w that the normalized elastic strain energy depends on the relative length of the cylindrical inclusion for the length-radius ratio l/a < 2, This stra in 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 re aches its steady state value. Several deformation features of this non-clas sical inclusion-matrix system are discussed. The work of this paper also pr ovides a quantitative solution in the investigation of the propagation of s train discontinuity observed during thermoelastic phase transformation in s olids such as TiNi shape memory alloy wires. (C) 2000 Elsevier Science Ltd. All rights reserved.