An understanding of the nature and conditions of nonlinear processes in open systems is important for modulation of the microstructure of solids at a new level of complexity. We demonstrate that cavitation generated by high intensity ultrasound (HIUS) triggers nonlinear processes in microparticles and layers of titanium. We reveal a non-monotonic dependence of the size of grains in the treated solids on sonication time, and oscillation of titanium grain sizes vs. time of ultrasonic treatment, indicating the influence of two opposing forces: cavitation driven impact of shock heating and shear stress on surfaces. These nonlinear self-organization processes in solids promise new microstructured materials with applications among others in bio- and geosciences.