Nonlinear implementations of acoustic diodes are inherently nonreciprocal and have received continuous attention from the beginning of the research boom for acoustic diodes. However, all the reported nonlinear schemes usually have the shortcomings such as low transmission ratio, action threshold, lack of stability and cumbersome setups. In the present design, we take advantage of extraordinarily large contact acoustic nonlinearity which is several orders of magnitude stronger than material nonlinearity. It is theoretically found that the spectra of the transmitted wave depend on the contact time. It is proven experimentally that the contact nonlinearity can be tamed by adjusting the driving amplitude, the static stress and the elastic constants of the materials. In order to build a compact acoustic diode, a sub-wavelength filter with a sandwich structure is designed. The total length of the acoustic diode is only three eighths of the incident wavelength. The amplitude-dependent behavior of the device exhibits similarities with electronic diodes. A more than 50% transmission ratio is obtained. A robust, stable, compact, highly efficient and solid-state acoustic diode is realized.