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A mathematical model is presented for the dynamic response of contractile fiber bundles embedded in an elastic medium. The fiber bundle is assumed to consist of a parallel array of contractile fibers made from contractile shape memory alloy wires of a few mills in diameter. The proposed model considers the electrically induced (ohmic heating) contraction of the fibers. A model is then presented for the electro-thermo-mechanics of such SMA assemblies including the heat transfer effects. For the proposed model, we consider the fiber bundle of SMA to be electrically insulated from the host elastic medium by means of a dielectric liquid to enhance the transfer of heat from the SMA wires to the host medium. The host elastic medium acts as a heat sink to quench the SMA wires during the power-off cycle, mainly by conduction heat transfer. Thus, the fibers can be electrically heated and subsequently contracted to compress the elastic medium. Design details are first described. In essence the dynamic behavior of the assembly depends on the interaction between the current supplied to the wires and the heat transfer from the wires to the elastic medium. Further, a mathematical model is presented to simulate the electro-thermo-mechanics of expansion and contraction of such assemblies. The proposed model takes into account all pertinent variables such as the strain (epsilon) , the temperature of the fibers T(t) as a function of time t, the elastic medium initial temperature T0, the martensite fraction (xi) , the elasticity of the host medium and the overall heat transfer coefficient h. Numerical simulations are then carried out and the results are displayed in the form of graphs. Computer simulation have been performed for a 1 meter aluminum cylinder of 50 mm in diameter with an elastic modulus of 70 GPa, with 2400 embedded SMA wires of diameter 0.254 mm under a duty cycle of 10 seconds on followed by 20 second off, to allow the temperature of wires to drop back to the martensitic phase. The dynamic response of such assemblies appear to be quite robust for a number of engineering applications.
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