Geomaterials possess a variety of remarkable nonlinear elastic properties: hysteresis with end-point memory [1], variation of attenuation and sound velocity with strain [2], strong dependence of elastic and loss constants on pressure, humidity, and pore fluids [3], long-time relaxation phenomena (slow dynamics) [4], and trivial variation of resonance frequency with strain [5].

These quantities depend strongly on the way rocks are cemented together, their porosity, and their permeability.

Remarkably, even until recently, a precise classification of the nonlinear dynamic phenomena in these materials did not exist. 

Only recently did a careful set of  resonance bar  experiments [6,7] finally establish two distinct regimes  see figure below: (1) a low strain regime where Landau (non)linear elasticity dominates—Landau theory is a power series expansion of Hooke’s law—and (2) a higher strain regime—a microstrain or so for Fontainebleau and Barea sandstones—where nonequilibrium process is excited and memory/slow dynamics is observed. In this regime an entirely new and additional mechanism for the downward frequency shift is now involved and Landau theory breaks down and remarkably little quantitative data exists.

Untangling the nonlinear and nonequilibrium processes in this regime will be essential to understanding the equation of state and modeling the behavior in these materials and is the focus of my current research in this field.