Pseudoelastic deformation of shape memory annular plates subject to normal tractions

The pseudoelastic deformation of shape memory annular plates subject to traction loads is investigated. Pseudoelastic behavior of the shape memory materials is modeled by a J2-type deformation theory incorporating an internal variable to accommodate the history-dependent hysteresis behavior.; The plane stress and plane strain responses of annular plates subject to forward transformation are obtained. The effective stresses are found to be non-increasing along radial direction analytically, which implies that the maximum effective stress is always located at the inner boundary of the plate. Therefore the forward transformation will initiate at the inner boundary and complete at the inner boundary first upon increasing traction loads. This enables us to study the fully martensite loops comprised of the load pairs just enough to complete martensitic transformation. Further parametric studies on these loops by varying material constants and geometry are performed. The structure maps partitioning the load in the {lcub}pi, p o{rcub} plane into different phase regions are obtained, and the effect of the geometry of the annulus on the partitioning is studied. The stress fields are obtained numerically by the shooting method.; For arbitrary traction histories, an iterative finite difference scheme is developed to solve the plane stress responses. The stress solution is integrated using the equilibrium equation and the compatibility equation with given transformation strain field. A nonlinear equation on transformation strain is obtained. The equation is discretized with the finite difference scheme and solved by Newton's iteration. The numerical results from the iterations agree with the shooting results for global loading and global unloading solutions. The history dependence of stress and martensitic fraction, the non-monotonousity in effective stress along radial direction and the movement of phase interfaces are presented.