Abstract: The variations in the constitutive characteristics of hard and brittle materials processed under ultrasonic vibration are researched based on the nonlocal theory in order to explore the high efficiency and ductility of ultrasonic vibration processing. The kernel function formula is deduced by analyzing the kernel parameters. The effects of internal and external characteristic variables, such as grain space, amplitude and frequency of ultrasonic vibration, on the nonlocal kernel function are systematically studied through numerical simulation. The theoretic results about the influence of ultrasonic vibration on the kernel function are verified in uniaxial tensile experiments. The research results show that, in terms of the effects of amplitudes and frequencies on the kernel function, there appears a shape of the downward parabola and there exists a critical value. In the experiment of tensile rupture, the practical influences of amplitudes and frequencies agree with the theoretic results deduced by numerical simulation. The fracture stress is minimal when the amplitude is 14. 94 μm and the frequency is 35 kHz. This study of the nonlocal elastic kernel function under ultrasonic vibration ensures an accurate understanding of the influences of ultrasonic vibration on the constitutive characteristics of materials, and provides the optimal parameters for ultrasonic vibration processing.

Key words: mechanics, nonlocal theory, elastic kernel function, elastic kernel parameter, ultrasonic vi- bration amplitude, frequency