In the last years experiments of cavitating water and of explosions of foils in water have provided possible evidence for production of stable, unstable and articial nuclides induced by ultrasounds and shock waves, i.e. for nuclear reactions induced by pressure waves (piezonuclear reactions). We propose a possible mechanism for the explanation of these ndings, that is constituted by two parts: a classical one, based on the bubble implosion due to cavitation, and a non-classical, related to a possible breakdown of Lorentz invariance for nuclear interactions. Such a mechanism allows one to get precise predictions on the values of energy and power needed to carry out experiments with the commercially available sonotrodes and to get piezonuclear reactions in a reproducible way.