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In this paper, we develop a complete mathematical model of a shape memory alloy (SMA) wire actuated by an electric current and a bias spring. The operation of the SMA actuator involves different physical phenomena, such as heat transfer, phase transformation with temperature hysteresis, stress-strain variations and electrical resistance variation accompanying the phase transformation. We model each of these phenomena in a modular fashion. A key feature of the proposed model is that one or more of its modules can be extended to fit other SMA applications. At the heart of the proposed model is a differential hysteresis model capable of representing minor hysteresis loops. We generate the temperature profile for the hysteresis model using lumped parameter analysis. We extend the variable sublayer model to represent actuator strain and electrical resistance. This model can be used to develop a position control system for the actuator. Simulation results from the model are found to be in good agreement with experimental data.