Test of hyperelasticity in highly nonlinear solids: sedimentary rocks

We report measurements of three-wave mixing amplitudes on systems whose third order elastic constants have also been measured by means of the elastoacoustic effect. Because attenuation and diffraction are an important aspect of our measurement technique we analyze our results using a modified Khoklhov-Zabolotskaya-Kuznetsov equation in the frequency domain. We find that the value of beta so deduced for polymethyl methacrylate agrees quite well with that predicted from the stress dependent sound speed measurements, establishing that polymethyl methacrylate may be considered as a hyperelastic solid. The beta values of sedimentary rocks, though they are typically 2 orders of magnitude larger than, e.g., polymethyl methacrylates, are still a factor 3-10 less than those predicted from the elastoacoustic effect.