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This work describes several physical models of the mechanical properties of rocks resulting in macroscopic nonlinear behavior due to their mesoscopic-scale structure. Theoretical models include Hertzian grain contacts with multiple scales and hysteretic properties. A significant addition to the highly nonlinear response in these materials are fluids contained in the soft bond system. CP524, Nonlinear Acoustics at the Turn of the Millennium: ISNA 15 edited by W. Lauterborn and T. Kurzdoi:10.1063/1.1309181 fatcat:xtodkny4mraudfeq5ikqblsovi