Prediction of wooden strength - a limit analysis approach

The excellent mechanical and physical properties of wood combined with the general trend of growing environmental awareness in civil engineering have led to an increasing demand for wooden building structures in recent years. Nevertheless, wood as structural bearing material is often countered with skepticism and therefore it is not used as extensively as its very good material behavior would suggest. Besides building physics and construction reasons, the main cause of this skepticism is the quite complex material behavior of wood, which is the reason that design concepts for wood have so far not achieved the prediction accuracy of those from other building materials. This is the main motivation for the proposed work, which aims at a new approach to understand and estimate failure mechanisms and the strengths of wood. Since failure initiation and crack formation is strongly influenced by the complex material system of wood, exhibiting cellular and layered structures on different length scales, a mechanical concept in which these different microstructural characteristics are incorporated appears to be necessary. Thus, the division of wood into meaningful levels of observation is the first objective of the proposed work. At each level, failure modes and strength properties are to be determined by means of numerical methods, and the obtained information is to be transferred - and will serve as input - to the next higher level of observation. For this so-called upscaling, at the Institute for Mechanics of Materials and Structures, a numerical concept based on the extended finite element method is currently in development, which is able to describe failure (even cracking mechanisms) of wood very accurate. For a comprehensive description of the strength behavior over several levels of observation, however, this method alone seems to be insufficient and inefficient. For this reason, within the proposed work, numerical limit analysis approaches will be developed and applied for the first time to wood, complementing the overall multiscale `damage` concept successfully. This method exclusively focuses on the time instant of failure, and delivers lower- and upper bounds for the ultimate strength of the considered material structure. Compared to conventional approaches, where the complete load history has to be considered and, in order to predict the correct failure mechanisms, proper regularization techniques must be used, limit analysis approaches are much more stable and efficient. The extension of existing limit analysis formulations by implementing orthotropic material behavior and appropriate boundary conditions, taking non-associative plastic flow into account, and the application to wood cells is the main objective of the proposed work. Finally, new insights into failure mechanisms of wood will be gained and a new numerical tool for predicting wooden strength will be available.

Traditionally, wood as a structural building material has mainly been used in rural areas for one- or two-storey residential buildings or simple halls and stables. In recent years, this situation has changed dramatically. The excellent mechanical and physical properties of wood, combined with the general trend of growing environmental awareness, have put timber structures into the focus of private as well as public building developers not just to realise small buildings, but to use wooden building elements for highly sophisticated engineering structures. For example, a24-storey wooden skyscraper will be completed in Vienna in 2018, which, with a height of 84 m, will be the tallest wooden skyscraper in the world. Such projects could, or respectively can, only be realised when the mechanical behaviour of this complex material is well understood. This has been the motivation for the present work, which aims at the development and assessment of new computational methods enabling better predictions of the mechanical behaviour of wood. Based on such methods, the great mechanical potential of the raw wooden material should be much better utilised.Within this work, three such computational methods have been investigated: an extended finite element approach able to describe brittle failure in wood; a newly-developed limit analysis approach, exclusively describing ductile failure; and an approach based on continuum micromechanics. All three methods were applied to microstructures of wood, like the well known honey- combed wood cells or the layered structure of early and latewood, respectively. Finally, the failure behaviour of these structures was obtained for a range of different loading states. The results of the different methods were compared to each other and to experimental results, allowing to discuss the strengths and weaknesses of the three computational methods, and to evaluate their applicability to wood. The extended finite element method is a powerful technique that allows for a very realistic description of strength-governing processes. Nevertheless, its complexity and high computational effort prevent widespread use in the engineering field. The plastic limit anal- ysis and elastic limit approaches, however, show good predictive performance compared with the extended finite element method, coupled with excellent efficiency and stability. In this study it is found that together, the latter two approaches are able to enclose the experimentally-obtained failure regions for clear wood almost perfectly, while also delivering new insights with respect to the ductile failure potential of wood.The conclusion can be drawn that there exist promising computational methods that are capable of delivering reliable strength information for wood and, subsequently, will enable effective strength predictions for wooden boards and wood-based products. Finally, this work is intended as a contribution to performance-based optimisation of wooden structures, a necessity for wood to become competitive with respect to other building materials.