Full elastic properties characterization of wood by ultrasound using a single sample

This paper focuses on the characterization of the three-dimensional elastic properties of wood materials using the propagation velocity of ultrasonic waves in the context of the inspection and diagnosis of timber structures. The scientific innovation consists in exploiting only the velocities of the compression (P) waves and using a single sample. From a three-dimensional formulation of Hankinson and an analytical development which allows to define the relations between the properties of elasticity and the velocities of ultrasonic waves, the twelve elastic constants are determined by means of an optimization procedure. The experimental validation on a Douglas fir cube allows to have the three moduli of elasticity \(\left( {E_{\text{L}} ,E_{\text{R}} ,E_{\text{T}} } \right)\) $\left(E_{\text{L}},E_{\text{R}},E_{\text{T}}\right)$ , the three shear moduli \(\left( {G_{\text{LR}} ,G_{\text{LT}} ,G_{\text{RT}} } \right)\) $\left(G_{\text{LR}},G_{\text{LT}},G_{\text{RT}}\right)$ and the six Poisson’s ratios \(\left( {\nu_{\text{LR}} ,\nu_{\text{LT}} ,\nu_{\text{RT}} ,\nu_{\text{RL}} ,\nu_{\text{TL}} ,\nu_{\text{TR}} } \right)\) $\left({\nu }_{\text{LR}},{\nu }_{\text{LT}},{\nu }_{\text{RT}},{\nu }_{\text{RL}},{\nu }_{\text{TL}},{\nu }_{\text{TR}}\right)$ . The longitudinal modulus \(\left( {E_{\text{L}} } \right)\) $\left(E_{\text{L}}\right)$ is more than eight times greater than the radial modulus \(\left( {E_{\text{R}} } \right)\) $\left(E_{\text{R}}\right)$ , which is more than two and a half times greater than the tangential modulus \(\left( {E_{\text{T}} } \right)\) $\left(E_{\text{T}}\right)$ . For the shear moduli, we obtain \(\left( {G_{\text{LR}} > G_{\text{LT}} > G_{\text{RT}} } \right)\) $\left(G_{\text{LR}}>G_{\text{LT}}>G_{\text{RT}}\right)$ . The Poisson's ratios meet the requirements of energy deformation positivity and stiffness matrix inversion. The values of the elastic constants obtained are in line with those from the literature.