Modeling of the Thermomechanical Response of Active Laminates with SMA Strips Using the Layerwise Finite Element Method

A study on the effective thermomechanical response of a composite laminate with shape memory alloy (SMA) layers based on the implementation of the layerwise laminate theory in the finite element method is carried out in this paper. The SMA thermomechanical constitutive response is based on a thermomechanical model recently developed by Boyd and Lagoudas. The numerical implementation of the constitutive model is based on a return mapping integration algorithm which is employed in studying the SMA response characteristics in the composite laminate under thermal loading. In modeling the laminate, a displacement based finite element approach is used in conjunction with the layerwise laminate theory of Reddy, incorporating piecewise continuous distribution of transverse strains through the thickness. As an illustrative example, the deformations caused by two prestrained SMA strips placed symmetric to the mid-plane of an elastic plate, when thermally activated are studied. The top SMA strip starts transforming from the martensitic into the austenitic state upon actuation through resistive heating, simultaneously recovering the prestrain, thus causing the laminate to bend. A parametric study investigating plane strain and generalized plane strain is carried out, and the accuracy of the results is compared with the commercial finite element code ABAQUS. The main feature of the presented methodology is an accurate evaluation of actuation stresses in the SMA strips, efficiently combining the layerwise geometry with the finite element method.