Constitutive modeling and structural analysis considering simultaneous phasetransformation and plastic yield in shape memory alloys

Abstract

The new developments summarized in this work represent both theoretical andexperimental investigations of the effects of plastic strain generation in shapememory alloys (SMAs). Based on the results of SMA experimental characterizationdescribed in the literature and additional testing described in this work, a new3D constitutive model is proposed. This phenomenological model captures boththe conventional shape memory effects of pseudoelasticity and thermal strainrecovery, and additionally considers the initiation and evolution of plastic strains.The model is numerically implemented in a finite element framework using areturn mapping algorithm to solve the constitutive equations at each materialpoint. This combination of theory and implementation is unique in its ability tocapture the simultaneous evolution of recoverable transformation strains andirrecoverable plastic strains. The consideration of isotropic and kinematic plastichardening allows the derivation of a theoretical framework capturing the interactionsbetween irrecoverable plastic strain and recoverable strain due to martensitictransformation. Further, the numerical integration of the constitutive equations isformulated such that objectivity is maintained for SMA structures undergoingmoderate strains and large displacements. The implemented model has been used toperform 3D analysis of SMA structural components under uniaxial and bendingloads, including a case of local buckling behavior. Experimentally validated resultsconsidering simultaneous transformation and plasticity in a bending member areprovided, illustrating the predictive accuracy of the model and its implementation.