Internal Residual Stress Patterns in Tree Stems

Abstract

Kubler (1959a, b) derived mathematical expressions for the internal stress increments induced by growth stresses in each small growth increment at the periphery of tree stems. His continuum mechanical arguments were based upon the equilibrium of suitably chosen elements, and wood was modeled as an elastic transversely isotropic material. Kubler (1959a, 1986) gives an excellent review of earlier work on this subject. He also pointed out the added protection which these residual stresses provide against damage by wind loads on the tree. The longitudinal stress at the periphery serves as a “pre-stressing” system against excessive compressive stress acting upon the stem opposite to the wind direction, while the tangential compressive stresses at the periphery counteract cracks induced by frost and drying or heating which might cause the tree to dry out.