Dynamic elastic anisotropy and nonlinearity in wood and rock

Abstract Ultrasonic techniques are used to characterize the anisotropic and nonlinear elastic behavior of wood and rock and to interrogate the structural properties of these materials. For elastic anisotropy two types of experiments are performed, namely qP-wave velocity measurements on spherical samples in about 100 directions of propagation rather regularly sampled in space, together with S-wave birefringence measurements in a few directions on additional samples. For nonlinear elasticity, acoustoelastic experiments were conducted, consisting in P and S-wave velocity measurements under controlled confining pressure. The experimental results show that wood exhibits much larger elastic anisotropy, but much weaker elastic nonlinearity than rock. For instance, the deviations from isotropy in wood can reach 70%, whereas in rock, typically, it can hardly exceed 20%. In contrast, regarding nonlinearity the increase of P or S-wave moduli per unit confining pressure in wood is always smaller than 30, in the radial direction, or 10, in the longitudinal and transversal directions, whereas it can reach roughly one to a few hundreds in rock. These contrasted behaviors can be simply explained by structural considerations. Thus, the exceptionally strong elastic anisotropy of wood is due to the strict structural alignment of its constituents, that is to say to the preferential orientation of the anatomical elements (tracheids, fibers, ray cells, vessels etc.) for ‘textural’ anisotropy, and to the cellular wall organisation for ‘microstructural’ anisotropy. In comparison, rock only exhibits a rough statistics of the orientation distribution function of its constituents, mainly the grain minerals, the pores and the cements. In contrast, the strinkingly strong nonlinear elastic response of rock, a wellestablished classical observation, is due to the presence of compliant mechanical defects (cracks, microfractures, grain-joints etc.). Such features are practically nonexistent in wood which explains its weak nonlinear response.