Developing the orthotropic linear-elastic model for wood applications using the FE method

Abstract

The purpose of this work is to develop the three-dimensional (3D) finite element (FE) modeling approach for the linear mechanical behavior of the wood material. The developed framework consists of implementing the 3D constitutive equations using the linear elasticity theory. Wood is a complex, porous, fibrous, inhomogeneous, highly anisotropic material. Various wood materials are considered, such as poplar, spruce, and maple specimens to validate the applicability of the FE modeling. The framework is implemented in explicit code, written in Fortran language, and based on the PETSc library. To that purpose, using up-scaling methods, such as the homogenization technique that allows the prediction of the macroscopic property of materials, in our case the effective Young's modulus, is investigated. A numerical approach to control the equivalent micromechanical properties is presented using a representative elementary volume (REV) concept. Here, we investigate the convergence trend of material properties and structural geometries according to REV size. This framework aids considerably in predicting the mechanical properties of a given material microstructure. In order to determine the mechanical properties of the wood material in its anisotropic direction, the traction and compression loadings were performed using numerical tests. The FE modeling of some cases is presented for the final validation.