Finite Strain Shape Memory Alloys Modeling - Scuola di Dottorato in ...

with R a material parameter defining the radius of the elastic domain and( tr )dev( T)= T− 1 T 1 is the deviator of the tensor T .3The quantity T is the thermodynamic associated variable to the symmetrictransformation rate tensor dt.Here, the derivative of the limit function f with respect to the dual variable definesthe direction of the internal variable increment , while ζ is the plastic consistentparameter.The limit surface defines the limit of the elastic domain. Inside the surface, that iswhen f < 0 , the internal variables do not vary, so that the plastic multiplier ζ iszero. Along the surface, that is when f = 0 , there is a variation of the internalvariables and the plastic multiplier is different from zero. Points outside of the limityield are not admissible.The described cases are summarized introducing the Kuhn-Tucker conditions ζ ≥0 f ≤ 0 ζ f = 0(4.40)that complete the model. The fulfillment of these conditions allows to evaluate theplastic multiplier and, as a consequence, the internal variables evolution.The so defined model can be classified as an associated model because the limitsurface governing the onset of the plastic deformations is assumed to be coincidentwith the plastic potential defining the plastic flow direction.It is well-known from experimental evidences that shape-memory materials,expecially NiTi and CuZnAl alloys, exibith a tension-compression asymmetry intheir phase transformation behavior which is not displayed by the here chosen ‘vonMises’ criterion. However the framework of this model also allows different phasetransition criteria which account for SMA tension-compression asymmetry.72