Numerical modeling of the thermomechanical behavior of shape memory alloys under finite deformations | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 24 > №3 / 2018 / Pages: 461-476

Numerical modeling of the thermomechanical behavior of shape memory alloys under finite deformations


In the framework of finite deformations theory a model of the behavior of shape-memory alloys (SMA) in view of the austenite-to-martensite phase transition and plastic deformation is constructed. All the nonlinear relations that occur under finite deformations are linearized, an approach based on the kinematics of superposition of small deformations on finite ones is used. It is assumed that the rates of change in the elastic, temperature, phase, structural and plastic deformations are additive. To describe the change in phase and structural deformations a simplified version of the model of nonlinear deformation of the SMA generalized to finite deformations is used. We take into account the shift of characteristic temperatures of the phase transition in the loaded material and also the dependence of the elastic moduli on the fraction of the martensitic phase. To describe the elastic behavior of the material a simplified Signorini law is used. The statement for the boundary value problem in differential form and the variational formulation in the Lagrange form are obtained. As boundary value problems we consider problems on the cantilever beam bending and torsion of a cylindrical sample of SMA. At the initial time the samples clamped at the left end face are in the austenitic state. To the right end the forces causing bending/torsion are applied, so the elastic and after the yield point plastic deformations appear in the material. After that at the same temperature the samples are partially unloaded, then they are cooled under the load with the phase and structural strains occurred as a result of direct martensite transition. The problems are solved in three-dimensional formulation by the finite element method using the step-by-step procedure. The distributions of the intensity of plastic, phase and structural deformations and the intensity of stresses are obtained.