274 M. Kaliske and D. Konopka Fig. 31.1 Shear test of adhesive-wood joints (glutin-based glue and European beech): (a) experimentally tested specimen [9]; (b) shear stress (τTL) propagation from initial condition (uL =0 mm) over peak condition before failure (uL =0.145 mm) until final condition (uL =0.5mm); (c) effect of three different moisture levels (RH=35%MC=6.8%, RH=65%MC=12.1%, RH=95%MC=23.8%) on the shear stress-relative displacement relation in the joint [11] When wooden structures are exposed to water vapour, moisture is absorbed via the surface and transported inside the material. Different models with different simulation effort and accuracy exist. A realistic model with a two phase, i.e. multiFICK’ian moisture transport of vapour and bound water is applied for the investigated sensitive objects [6]. The mechanical and hygric effects are mutually dependent. The processes of swelling and shrinkage (hygro-expansion) take place in every wooden construction and can cause decisive stresses, when the free hygro-expansion is constrained. The effect is modelled with differential swelling/shrinkage values (percent swelling/shrinkage per percent moisture change). Another effect is the change of material properties with changing moisture content, which is as well considered for the material models. With increasing moisture content, elastic and strength values decrease. Since the material properties of wood are defined by the microstructure, all input quantities of the models additionally depend on the wood species. The surface resistance with respect to the emission of water vapour is considered by hygric convective surface elements. Models for the influence of the buffering effect, based on the boundary layer theory as well as models for shellac varnish with specific permeabilities are available and applied in the simulations [7, 8]. The contribution of the surface coatings on the mechanical load bearing behaviour of the structure is rather marginal, due to their small thickness. It might become relevant for the analysis of grounded (gesso layer) panel paintings with thicker coatings. Recent investigations deal with the development of multi-FICK’ian hygro-mechanical models for glutin-based bond lines. A cohesive element model, based on [5] is modified by adding features to simulate the mechanical behaviour of and the moisture transport in the joint. The joint, which includes one layer of adhesive and two layers of transition zones, is simplified by using a single layer of cohesive elements. The material properties of the adhesive and the transition zones are assigned to the cohesive element. This method decreases computational effort with a lesser number of material and element layers, while still maintain the reliability of the model. The investigated glues are gelatine-based adhesives, which are often used in wooden cultural heritage objects found in museums and collections. The hygro-mechanical properties of gelatine-based adhesives base on experimental investigations in [9, 10]. The element and material formulations are described in [11]. The new bond line model is validated by numerical investigations of two wood species, European beech (Fagus sylvatica L.) and Norway spruce (Picea abies L.), based on own and further experimental studies available in the literature. The simulated specimens contain a single bond line of animal adhesive. Hygro-mechanical shear tests (Fig. 31.1) and diffusion experiments are simulated and compared to the experimental results. Finally, the methods are applied on the hygro-mechanical structural analysis of a clavichord. The structure is mechanically loaded by the tensioned strings and the pins that carry the string load into the instrument. With respect to the hygric loading, an alternating climate with a changing ambient relative humidity (RH) is simulated. 31.3 Results and Discussion The results of the validations show that under mechanical loading, the numerical simulation of fracture under tension and shearing are in agreement with the experimental results. Under moisture loading, however, the numerical results are diverse in comparison to the experimental results. The reason for this difference is primarily due to the incomplete experimental data which are served as the input parameter in the numerical simulation.
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