1. The RVE has the same elastic constants and fiber volume fraction as the composite. 2. The three-dimensional elastic constants of materials can be measured using the composite materials. 3. The elastic constants often change with depth, due to the changing properties of the material. 4. The key result here is a negative elastic constant created from resonant frequencies of the material. 5. It turns out that these are the material's mass density and its elastic constant . 6. For a sphere of radius R and elastic constants E, \ nu this Hertzian solution reads: 7. Rayleigh waves have a speed slightly less than shear waves by a factor dependent on the elastic constants of the material. 8. Then apply a nonlinear inversion algorithm to find the elastic constants from the measured natural frequencies ( the inverse problem ). 9. This happens for instance if the bodies are mirror-symmetric with respect to the contact plane and have the same elastic constants . 10. In this case one may need to use the full tensor-expression of the elastic constants , rather than a single scalar value.
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