Three wave mixing test of hyperelasticity in highly nonlinear solids: Sedimentary rocks

Abstract

Measurements of three-wave mixing amplitudes on solids whose third order elastic constants have also been measured by means of the elasto-acoustic effect are reported. Because attenuation and diffraction are important aspects of the measurement technique results are analyzed using a frequency domain version of the KZK equation, modified to accommodate an arbitrary frequency dependence to the attenuation. It is found that the value of β so deduced for poly(methylmethacrylate) (PMMA) agrees quite well with that predicted from the stress-dependent sound speed measurements, establishing that PMMA may be considered a hyperelastic solid, in this context. The β values of sedimentary rocks, though they are typically two orders of magnitude larger than, e.g., PMMA’s, are still a factor of 3–10 less than those predicted from the elasto-acoustic effect. Moreover, these samples exhibit significant heterogeneity on a centimeter scale, which heterogeneity is not apparent from a measurement of the position dependent sound speed.