Active shape/stress control of shape memory alloy laminated beams

This paper deals with a study of the modeling and active shape/stress control of laminated beams subjected to the static loading with integrated/embedded shape memory alloy (SMA) layer. A one-dimensional shape memory alloy model is proposed which is able to simulate main aspects of SMAs including martensite transformation/reorientation, shape memory effect and pseudo-elasticity. In particular, the model includes a ferro-elasticity effect which is essential for accurate prediction of behavior of pre-stained SMA layers. Euler-Bernoulli beam theory and von Karman geometrically non-linearity are utilized to describe displacement and strain fields of laminated beams consist of SMA and elastic layers. A finite element method along with an iterative incremental approach is developed to treat material and geometrical non-linearities of the governing equations of equilibrium. To validate the proposed SMA model, numerical results of partial uniaxial tension tests are compared with experimental data in the literature which show excellent correlations. Influence of pre-strain, temperature and location of SMA layer on the active shape/stress control of SMA laminated beams subjected to different thermo-mechanical loading paths are put into evidence via a parametric study, and pertinent conclusions are outlined.