Effects of body stiffness on propulsion during fish self-propelled swimming

Many fish propel themselves using wave-like lateral flexion of their body and tail in the water. The undulatory body is driven by the distributed muscles, and locomotion is achieved by internal muscular stimulation and the external action of the fluid. As one of the material properties, the stiffness of the body being propelled plays an important role in the deformation process, especially for the muscle power input and phase lag. In this paper, a three-dimensional self-propelled elongated body model is employed to numerically investigate the effects of stiffness on the propulsion performance, including the forward speed, energy consumption, and energy-utilization ratio. According to various deformation characteristics and energy-utilization ratios, three deformation modes corresponding to high, medium, and low stiffness are identified. Our results indicate that a deforming body with medium stiffness has the highest efficiency, and its corresponding deformation is closest to that of fish in nature. When the stiffness of the fish body is higher than the normal level, more muscle energy is needed to sustain the tail beating of the same amplitude. A lower level of stiffness produces a more obvious phase lag in the fish body, which might lead to slow control responses. We also show that the stiffness of the fish body affects the scaling relationship between the swimming speed and the tail beating velocity. The upper and lower limits of the scaling exponent correspond to high and low levels of stiffness, respectively, and are also affected by the wavelength of the muscle contraction.