Numerical Simulation of Stress Wave Propagation in the Three-Layer Medium Structure of Standing Trees

Abstract

Based on the theory of stress wave propagation in solid media, this paper conceptualizes standing trees as a three-layer composite material comprising the pith, heartwood, and sapwood. Assuming that standing trees exhibit orthotropic anisotropy, the propagation process of stress waves within the trees is simulated and analyzed using the finite element simulation software. The paper investigates the effects of diameter at breast height (DBH) of 40-year-old standing larch trees and the proportional composition of pith, heartwood, and sapwood on the propagation of stress waves. The results reveal that, despite variations in DBH and the relative proportions of the three components, the overall propagation patterns of stress waves remain largely consistent across models. Initially, stress waves propagate in the form of an inclined curved surface. As the propagation distance increases, the inclination of the wavefront gradually decreases, eventually approaching a plane perpendicular to the longitudinal axis of the standing tree.  When the DBH increases from 30 cm to 50 cm, the stress wave velocity rises significantly from 3,450 m/s to 3,620 m/s. Additionally, as the proportion of sapwood increases, the velocity increases from 3,529 m/s to 3,916 m/s. A strong correlation is observed between wave velocity and the compositional ratio of the three components, with a correlation coefficient  (R²) of 0.98.