Hybrid numerical method for the ultrasonic wave propagation velocity in orthotropic materials

This paper deals with a new hybrid method coupling an analytical and finite element approach for the calculation of the ultrasonic wave propagation velocity in orthotropic materials applied to timber elements. First, the method consists of integrating an analytical model described for orthotropic materials by considering a misalignment of the ultrasonic wave propagation direction with the main orthotropic reference. A second step calls for implementation in a finite element approach. This coupling allows for the computation of wave propagation velocity by assuming a heterogeneous material induced by means of a moisture content gradient in timber elements exposed to outdoor conditions inducing a non-homogeneous distribution of mechanical properties such as moduli of elasticity integrating the orthotropic character of wood. The result of this work proposes a highly efficient hybrid numerical approach, yet without solving the dynamic finite element problem, which typically requires a very long computation time while benefiting from a finite element support to project the different mechanical and hydric fields.