Phase-field theory for the description of the overdriven fracture in liquid (cavitation) in tensile pressure wave is developed. Various results from solid mechanics are transferred into mechanics of fluids. Thermodynamic potential is formulated that describes the desired tensile pressure–volumetric strain curve and for which the infinitesimal damage produces infinitesimal change in the equilibrium bulk modulus. It is shown that the gradient of the order parameter should not be included in the energy, in contrast to all known phase-field approaches for any material instability. Analytical analysis of the equations is performed. Problems relevant to the melt-dispersion mechanism of the reaction of nanoparticles on cavitation in spherical and ellipsoidal nanoparticles with different aspect ratios, after compressive pressure at its surface sharply dropped, are solved using finite element method. Some nontrivial features (lack of fracture at dynamic pressure much larger than the liquid strength and lack of localized damage for some cases) are obtained analytically and numerically. Equations are formulated for fracture in viscous liquid. A similar approach can be applied to fracture in amorphous and crystalline solids.
Available at: http://works.bepress.com/valery_levitas/53/