Chapter 31 Hygro-mechanical Modelling of Wood and Glutin-based Bond Lines of Wooden Cultural Heritage Objects Michael Kaliske and Daniel Konopka Abstract A comprehensive modelling of the transient hygro-mechanical behaviour of complex wooden structures by finite element method is targeted. New methods and material models for glutin-based bond lines are developed, since bond lines proved to have significant influence on moisture transport and fracture behaviour. The models are validated and applied to the structural analysis of wooden music instruments exposed to mechanical and hygric loadings. Keywords Finite element analysis · Hygro-mechanical coupling · Multi-Fick’ian moisture transport · Transient structural analysis · Wood-adhesive joint 31.1 Introduction In many cases, museums with collections of historical music instruments have the conflict between conservation of the original substance and maintenance of original use. Especially playable stringed keyboard instruments are complex wooden structures under heavy mechanical loading. Hygric loadings as alternating climate conditions induce additional mechanical loadings and influence the physical properties enforcing damages to the structure like large deformations and cracks. In a recent research project, the Institute for Structural Analysis is developing an objective simulation tool for museums, conservators and instrument makers in order to be able to evaluate wooden structures. The complexity of the investigated structures and materials need to be modelled in an efficient and reliable manner. Simplifications and assumptions have to be included. But often, oversimplifications are applied in recent numerical structural analyses of wooden structures. The time- and moisture-dependent material behaviour of wood as well as the mechanical and hygric characteristics (e.g. water transport) of bond lines and surface coatings, which have a significant direct or indirect contribution on the load bearing behaviour of the whole structure, need to be considered properly. In this paper, a short overview is given on the numerical models utilised in the software for the simulation of the load bearing behaviour at coupled mechanical and hygric loading. 31.2 Methods For the comprehensive structural-mechanical investigation of the whole construction of a complex wooden structure, like wooden music instruments, numerical methods are required. Therefore, the finite element method (FEM) [1] is utilised. In the following, the developed methods and time- and moisture-dependent material models of wood and bond lines are briefly introduced. They are used for the investigation of the moisture distribution, the state of deformation and the load bearing behaviour. The properties of loaded wood essentially depend on the type and direction of loading, respectively the material directions radial (r), tangential (t) and longitudinal (l). Compressively loaded wood, especially perpendicular to the grain, leads to ductile failure with plastic deformations beyond the elastic range. For the numerical simulation, a multi-surface plasticity model has been developed [2] and expanded to moisture dependency [3]. The elastic behaviour bases on the theory of orthotropic elasticity [4]. Exposed to tensile or shear loading, wood shows distinctive brittle failure. This property can be captured by interface-elements and corresponding moisture dependent material models [3, 5]. M. Kaliske ( ) · D. Konopka Institute for Structural Analysis, Technische Universität Dresden, Dresden, Germany e-mail: michael.kaliske@tu-dresden.de © Society for Experimental Mechanics, Inc. 2020 R. Barthorpe (ed.), Model Validation and Uncertainty Quantification, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12075-7_31 273
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