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

4.2 Constitutive ModelThe micromechanical behavior of crystal metals is assumed as the basis for thederivation of a new constitutive model for shape memory alloys. Nevertheless, itmust be pointed out that the plastic mechanism of deformation simply based oncrystallographic slips of the atomic planes results really different from thediffusionless thermoelastic martensitic transformation governing the phase transitionin the shape memory alloys. However, as for the modeling of the crystal metalplasticity, the SMA constitutive model considers the assumption of the localmultiplicative decomposition of the deformation gradient in the form:FX ( , t) = F( X, t) F( X , t)(4.3)etfor each material pointX ∈Ω, the reference configuration of the body. Feis relatedto the deformation caused by stretching and rotation of the material, Ftaccounts forthe inelastic flow associated to the phase transition in the SMA and F is the totaldeformation gradient. The multiplicative split of the deformation gradient in the formpresented in expression (4.3) is consistent with a large part of the literature on finitedeformationinelastic models (Lee,1969; Mandel, 1974).This decomposition introduces the idea of an intermediate configuration which canbe considered as the one associated to the body when the loads are removed and thetemperature is reduced to the initial one, thus releasing the thermoelastic strains.As a consequence, the intermediate configuration is obtained from the currentconfiguration by elastic destressing to zero stress. It differs from the initialconfiguration by a residual or inelastic deformation and from the currentconfiguration by a reversible or elastic deformation. Accordingly, it is implicitlyassumed that the local intermediate configuration defined bydeformation gradients F eandF is stress-free. Theconfiguration is not unique; in fact, arbitrary local material rotations can be58−1eFpare not uniquely defined because the intermediate