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

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 beta 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 beta 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.

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.