A simple strategy for constitutive modelling of timber

• Development of an orthotropic constitutive law for timber.
• Nonlinear finite element analysis of timber and engineered wood products.
• Capturing failure mode of timber using isotropic material models.
• Application of theory of composites for modelling timber behaviour.

This paper focuses on development of a simple technique for modelling anisotropic behaviour of timber and engineered wood products. In the proposed approach, timber is treated as a composite material comprising a matrix with smeared fictitious reinforcing fibres in the principal directions. The matrix is assumed to be isotropic with a piecewise continuous failure envelop in the bi-axial stress space and the reinforcements follow uni-axial stress–strain relationships with different strengths under tension and compression. The stress–strain relationship of timber is obtained by superimposing the constitutive law of matrix and the fictitious reinforcements based on the principles of compatibility and equilibrium. Such a modelling strategy provides a simple platform for calibration of the constitutive law against available mechanical properties of the timber in different directions (i.e. parallel or perpendicular to the grain). The proposed modelling technique is implemented in a finite element code and the developed analytical tool is verified by examples taken from the literature including bending tests on timber beams with notches and web openings, embedding tests on timber and push-out tests on TCC joints. It is shown that the proposed modelling strategy can adequately capture the mode of failure as well as the nonlinear behaviour of timber at local and global level.