Keywords: anisotropic material, multi-surface plasticity, brittle failure, cohesive elements, transport processes, hygro-mechanical coupling, uncertainty, fuzziness.

This paper discusses the numerical analysis of timber structures by means of the finite element method. Appropriate material models for wood, required for this kind of simulation, are scarcely published and often difficult to use with respect to their identification of input parameters and the application to three-dimensional structures. For this reason, material formulations are developed, which allow close-to-reality FE analyses of wooden structures, considering nonlinear stress-strain-relationships, failure due to compression, tensile or shear loading, inhomogeneities due to natural growth, influence of moisture content and uncertain material properties. These approaches are introduced within this paper.

In order to simulate the load bearing behaviour of wooden structures due to mechanical loading realistically, an appropriate formulation of the different characteristics of wood is of major importance. Elastic properties have to be described as being cylindrically anisotropic. Ductile behaviour under compression is captured by a multi-surface plasticity model which considers the anisotropic material strengths of wood and its post fracture behaviour. For better numerical handling, an approach, where as the single yield-surfaces of the plasticity model are combined by C₁-continuous transitions, is introduced. In order to consider brittle failure as a result of tension and shear loading, especially perpendicular to the grain, cohesive elements are applied. This material model is characterized by the coupling of the tension crack opening relation and the shear slide dependency. The analysis of the load bearing behaviour due to mechanical loading is also coupled to moisture changes. Hence, the physical characteristics of wood have to be included adequately into the material models. Therefore, hygro-mechanically coupled models are introduced to consider the influence of the moisture content on the mechanical characteristics.

For realistic computation, structural and material inhomogeneities are taken into account within the structural analysis. Due to the growth conditions of a tree, the grain course in wooden structural parts can differ. Especially branches, leading to knot holes, affect the mechanical properties. Therefore, an approach for the modelling of these growth inhomogeneities is presented. Moreover, the parameters of the material formulations are regarded as being uncertain. To consider subjective data and an insufficient experimental data base concerning wood, the alternative uncertainty model fuzziness is introduced to describe these uncertain parameters.

Although, the proposed formulations are still under development and part of ongoing work, they already provide an appropriate base to simulate the behaviour and failure of timber structures. The material models presented are practice-oriented due to the use of engineering material parameters.

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