Abstract
Numerical implementation of the thermomechanical constitutive response of shape memory alloys (SMAs) is performed using a return mapping integration scheme (Ortiz and Simo, 1986). The implementation is based on the framework of a thermodynamic approach proposed by Bo and Lagoudas (1994). Three models unified under the thermodynamic formalism, namely, Tanaka's exponential model (I 986), Liang-Rogers' cosine model (I 990, 1992), and Boyd-Lagoudas's polynomial model (1995), are implemented. Complex 3-D, 2-D plane strain and generalized plain strain, as well as 1-D material states are incorporated in the implementation. Flexibility is given in the general structure of the scheme, for future integration of other constitutive models. Feasibility of the numerical implementation is manifested in the analysis of two active composite problems. In the first problem, it is used in conjunction with the finite element method (FEM) to predict the thermomechanical response of an aluminum matrix / SMA fiber composite. Suitable tetragonal and hexagonal periodic arrangements are considered, and respective boundary conditions are established for finite element usage. An increase in the overall yield stress of the composite is shown and qualitative agreement is found relative to experimental results obtained from Taya et al. (1993). The second problem consists of an active composite beam, composed of aluminum matrix and embedded SMA wires along the length of the beam, under thermal activation. The numerical scheme is based on the finite element method formulated according to the layerwise plate theory (Reddy, 1987), which reduces the size of the problem computational-wise, relative to the classical 2-D finite element method. 2-D plane strain and generalized plane strain cases are calculated and compared to the results acquired from Euler-Bernoulii beam theory formulation. Similar displacement and stress fields are obtained for both layerwise cases, whereas Euler-Bernoulii results are found to be exceeding to layerwise calculations.
Qidwai, Muhammad Abu Bakar Siddiq (1995). Numerical implementation of shape memory alloy (SMA) constitutive response and structural analysis of active composites. Master's thesis, Texas A&M University. Available electronically from
https : / /hdl .handle .net /1969 .1 /ETD -TAMU -1995 -THESIS -Q23.