Induced-strain actuators, for example piezoelectric and electro-active polymer devices, can be bonded to elastic substrates to induce flapping-like motion to form synthetic wings. Ornithopters equipped with induced-strain actuated wings do not need conventional motors and mechanisms (i.e., revolute and prismatic), potentially saving weight and energy consumption, reducing mechanical complexity, and improving wing durability. By optimizing actuator placements, excitation amplitude and phase, substrate thickness/stiffness distribution, wing mounting position, etc., a mechanism-free wing may be able to reproduce features of natural flyers. In this research, a multi-physics strongly-coupled lumped parameter model is developed to predict the dynamic response of a mechanism-free wing, which is then used in ornithopter design and controller optimization, also termed control co-design. The modeling of an induced-strain actuated ornithopter wing involves modeling of fluid-structure interaction and circuit-actuator electromechanical coupling. The structural model of the composite wing with a customizable profile is based on the Rayleigh-Ritz method. The fluid-induced effects on the wings have several contributions such as added mass and damping, and quasi-steady and unsteady aerodynamic forces. The wing, fluid-induced effects, and circuit are integrated to derive the lumped parameter governing equations using Hamilton's principle. Since the structure, fluid, and circuit domains being all represented by the lumped-parameter subsystems, the coupling between different domains is clearly defined and exposed. The reducedorder model proposed in this paper is computationally efficient, suitable for trade studies and multi-disciplinary design optimization, and can be easily converted to state representation for controller development purposes.