Yield criteria for shape memory materials: Convexity conditions and surface transport

Dedicated to Professor Bogdan Raniecki on the occasion of his 70th birthday. Abstract: We study the yield conditions of phase transformation initiation for shape memory alloys exhibiting asymmetry between tension and compression. An extension of the choice of the classical invariant parameters such as those of Lode is proposed. A necessary and sufficient condition of convexity of these surfaces representing the elastic domain of austenite in the stress space, is established. Moreover the transport of these surfaces in the space of effective transformations strains of martensite is done. Hence, the duality between these two spaces is built. Some applications involving Cu–Al–Be and NiTi shape memory alloys end the purpose