Using Spatial Heterogeneity and the Inverse Method to Solve for the Elastic Constants of Wood and Wood Composites

摘要

Wood and wood-based composites have spatial heterogeneity that influences their mechanical properties. For solid wood, the most obvious heterogeneity is the growth pattern. This growth pattern is often simplified in the form of a cylindrical coordinate system (R, θ, L) with elastic moduli of E_R, E_θ, E_L, which are approximately proportioned 1.6:1:20 [1] based upon uniaxial tests. Oriented Strand Board (OSB) is a wood-based composite that has obvious heterogeneity of the individual wood strands (approximately 0.5 to 0.7 mm thick, 19 to 38 mm wide and 76 mm long). During the forming process of the composite panel, these strands are unevenly distributed in the plane of the composite panel (12.7 mm by 1.2 m by 2.4 m). This variation in distribution of strands leads to a variation in density, which results in variation in elastic moduli throughout the panel.To accommodate this spatial heterogeneity, a numerical technique was developed that allows for the spatial variation of the elastic constants. The numerical technique involves rewriting the well known load-displacement relation {p} = [k]~*{u} into {p} = [A]~*{D}, where p is the known load vector, u is the known displacement vector from tests, k is the stiffness matrix, D is the elastic constants, and A is an accumulation of the assumed strain fields B, measure displacements u, coordinate transformations T, etc. Because the system of equations in {p} = [A]~*{D} can be undetermined, a singular value decomposition is employed to solve for the material constants {D}.For solid wood, this numerical technique was applied to determine the elastic constants for a solid block of redwood that had changing principle material directions within the specimen [2]. For OSB, the density variations within a uniaxial tension specimen were measured and a linear relationship for modulus (E) as a function of density (p) (E=a_1~* ρ+a_0) was substituted into D and the constants, a_0 and a_1 were solved for [3].