The stability of a circular plate of shape memory alloy during a direct martensite transformation

In different formulations, analytical solutions are obtained of the problem of the axisymmetrical loss of stability of a circular plate of shape memory alloy undergoing a direct martensite transformation under a compression load. It is established that the solution based on the “fixed phase composition” concept gives an upper estimate of the critical load, while the solution based on the “continuing loading” concept gives a lower estimate. For a clamped plate, an intermediate solution is found using the “elastic unloading” concept that satisfies all the equations of the problem with zero variations in external loads and corresponds to a thickness of the additional phase transformation layer that is independent of the radial coordinate.