NON-LINEAR CONNECTION MODELS IN TIMBER ENGINEERING

NON-LINEAR CONNECTION MODELS IN TIMBER ENGINEERING Michael Dorn 1, Thomas K. Bader 2 ABSTRACT: In this contribution, a numerical model for connections in engineered timber structures, using specially designed connection elements, is presented. The model considers the non-linear load-displacement relation typical for many types of connections on different levels and is presented on the example of dowel-type connections. The structural levels investigated herein are a) the embedment behaviour of a dowel into wood; b) the behaviour of a singledowel connection; and c) a multi-dowel connection under a general load case typical for structural applications. A special characteristic considered in the formulation of the connector elements is the unloading behaviour, which is characterized by an initial high unloading stiffness but a very low stiffness when the load is fully removed. The latter is due to remaining permanent deformations in the wood as well as in the metal connector. The modelling approach was found to correlate well with experimental data and gave new insight in the behaviour of dowel connections, particularly as regards the unloading and reloading behaviour with alternating load directions on the single-dowel connection scale. KEYWORDS: Timber connection, non-linearity, load-displacement relation, plasticity, permanent deformations. 1 INTRODUCTION 12 Connections are used to mechanically combine two structural elements for a secure and reliable load transfer between the connected members. In engineered timber structures, timber elements are either directly or through a steel plate connected to each other, establishing socalled timber-to-timber or timber-to-steel connections, respectively. A large variety of connector types is available for timber structures, differing both in terms of principles of load transfer and also in terms of their strength, i.e. of their load transfer capacity. The behaviour of connections even affects the performance of timber structures, since connections can be designed to allow for high grades of ductility, which would not be available in the structural elements themselves. For the latter, dowel-type connectors are preferable since they allow for the introduction of high local forces into the wood in a concentrated way, and hence, are activating plastic material behaviour. The so-called embedment behaviour of wood, which describes the load transfer from a round, dowel-type, metal connector to the surrounding wood, which predominantly leads to compression stresses in the wood, typically shows a ductile behaviour, regardless of the global load direction with respect to the grain orientation. In addition, the use of metal connectors (dowels, bolts, nails) adds ductile 1 Michael Dorn, Linnaeus University, Sweden, michael.dorn@lnu.se 2 Thomas K. Bader, Linnaeus University, Sweden, thomas.bader@lnu.se deformation abilities in the plastic region when loaded in bending. Structural timber connections with dowel-type metal connectors are hence in general characterized by a nonlinear load-displacement relationship due to two reasons. Firstly, the wood is loaded in compression, which eventually leads to loading beyond the quasi-elastic limit and induces permanent deformations. Secondly, as soon as the metal connectors are slender, bending of the connectors leads to plastic deformations within the connectors themselves. In both cases, permanent, plastic deformations are encountered. Combined, this gives highly non-linear behaviour with potential room for ductility in the connection. In engineering applications, and also according to the Eurocode 5 [1] as the European design standard for timber engineering, connections are typically considered to have constant linear stiffness ( in the Serviceability Limit State and in the Ultimate Limit State), while the maximum allowed load level is limited by the characteristic load bearing capacity,, derived through a limit state analysis. This contribution aims at the development of a numerical model that is able to predict the non-linear loaddisplacement relationship of connections based on the behaviour of their components. The modelling of the single-dowel connector follows the approach of a beam on non-linear elastic foundation [1]. The specific objective herein is set to the development and application of a connector element able to consider the hysteresis behaviour in the component behaviour of timber connections due to plastic deformations. The connector element is herein further applied to studying

the peculiarities of dowel-type connections at three different structural levels: at the embedment behaviour, for single dowel connections, and for groups of dowels. A general introduction to the connection behaviour and characteristic properties on various structural scales is given in Section 2 before the experimental database is discussed in Section 3. Section 4 describes the connector element and its implementation in a finite element method framework, while the validation of numerical models using the connector element with experimental datasets is presented in Section 5. Modelling results as regards applications are given in Section 6, before the paper is concluded in Section 7. 2 CONNECTION BEHAVIOR The typical behaviour of dowel-type connections comprises a certain sequence, which can be observed in load-displacement diagrams. The main parts of interest are the stiff initial loading, a pronounced ductile load plateau and permanent deformations when unloading (see the red, orange and green parts in Figure 1, respectively; [2] provides a more detailed overview). Figure 1: Typical load-displacement diagram of a connection with the different sections highlighted: initial loading (red), load plateau and failure (orange), and un-/reloading paths (green) The initial stiff loading region is often considered elastic, while already at small loads permanent deformations are encountered, stemming from the deformations in the contact zone or from permanent, plastic embedment deformations in the wood. In the following, the loading is consequently considered non-linear with permanent deformations from the beginning onwards. In contrast to that, the unloading can be considered elastic and having approximately the same slope as the initial stiffness. This corresponds to the maximum stiffness of the connection and can be considered to be independent of the point of unloading (at small or large displacements). The load plateau is characterized by an approximately constant load level in the connection with smaller load drops or further increasing force at continuous loading, which leads to the final failure, typically in a brittle manner. These phenomena are observed on three characteristics structural levels of connections, which will be discussed in the following: On the level of embedment of a connector into the surrounding wood, the basic properties are determined: embedment stiffness as well as embedment strength. Embedment stiffness is defined approximately as the stiffness in the initial loading range, while embedment strength is defined as the maximum nominal embedment stress, i.e. the embedment load divided by the projected area of the connector, up to a certain connector displacement. The course of the load-displacement relation is however not exploited in practical applications and in the design rules given in design standards. Wood material properties and the surface characteristics in the connector-wood interface are the main influencing factors for the embedment behaviour. Considering a single-connector under bending, the loaddisplacement behaviour is further influenced by the cross-sectional properties, also described by the slenderness of the connector as well as by its material properties. Again, the load-to-grain angle considerably influences the connection behaviour. The final level to consider is the behaviour on the multiple-connector level with several connectors under a general load case (in case of plane loading conditions, a combination of normal and shear force and a bending moment). At this level, two relative deformations as well as a relative rotation are considered. 3 FROM EMBEDMENT TESTS TO STRUCTURAL DESIGN BEHAVIOUR The current design concept for connections with doweltype fasteners in the European timber engineering design standard Eurocode 5 [3], is making use of the abovedescribed three structural scales in a step-wise calculation procedure. The embedment behaviour (strength) is determined either from testing according to EN 383 [4] or directly taken from design equations given in Eurocode 5 [3]. The same applies to the yield moment of the metal connector. With the embedment strength and the connectors yield moment, the formulae for single-dowel connection behaviour (ultimate characteristic strength,, as well as stiffness in the serviceability,, and ultimate limit state, ) for arbitrary load-to-grain angles are evaluated. For the design of multi-dowel connections, only general design rules but no design equations are given in the standard. In general, the load levels of the individual dowels for a specific load case (including the load-tograin direction at each dowel) needs to be calculated in order to be able to compare these values to the corresponding single-connector strength. The compatibility of deformations is requested but only strongly simplified stiffness values for single-dowels not compatible with limit loads are provided.

Figure 2: Complementary approach for the characterization of connections: from the embedment behaviour to structural design A similar flow of calculations as suggested in the design standard is followed in the numerical model presented in the following. The individual levels of this complimentary approach are shown in Figure 2 as well as the steps that connect those levels. The modelling starts at the embedment of the connectors into the surrounding wood. This basic behaviour can be studied experimentally in a way that only limited influencing parameters are present. Particularly the load-to-grain angle is influencing the behaviour but also certain differences due to the material (wood species, engineered wood products) and the roughness characteristics of the dowels might be required to take into account. Experimental data of the embedment behaviour forms the starting point of the modelling approach, which is described next. 4 NUMERICAL MODEL All three structural levels discussed above have some common features, which the model takes into account, namely the strongly non-linear load-displacement relationship in component properties with an unloading path that is considerably stiffer than the initial loading path due to permanent deformations (see Section 2). This behaviour is considered in the model as follows (see Figure 3): - a non-linear force-displacement relation along the initial loading path; - a linear unloading path K un, with a stiffness similar to the initial stiffness K 0 at the beginning of the initial loading path; - remaining permanent deformations (plastic deformations) at load removal; and - almost zero stiffness,, close to the point of zero force when load reversal is occurring. On all three structural levels, failure of the connections due to e.g. splitting or other brittle failure modes with a fatal load drop are not taken into account; i.e. the connection is assumed to be ductile, which can e.g be achieved by adding adequate reinforcement measures. 4.1 Mathematical description The non-linear loading curve is defined by a sum over i exponential functions, reading as, / exp 1, (1) with the force (which could also be a stress or an internal force on the structural scale) being a function of the displacement (which could also be a rotation), the initial stiffnesses, and the associated factors for each exponential function i. The dimension of, is /, while has dimension of 1/. is defined with negative values. The regression function specified in Equation (1) allows for a good approximation of input data by using a suitable number of chain elements for an appropriate fitting and is hence adaptable to various situations. It furthermore follows the requirement of a non-linear, continuously monotonic curve. Figure 3: Principal non-linear load-displacement (F-δ) relation with the un- and reloading path and near-zero stiffness at the point of zero force, as considered in the modelling approach The stiffness of the connection,, is given by the first derivative of the load-displacement curve, reading as, exp. (2) It shows highest levels at zero displacement, where it becomes equal to the initial stiffness 0,. The unloading stiffness can arbitrarily be chosen by a single parameter. Herein, it is set equal to the initial stiffness, hence unloading occurs with the stiffness. In the case of full unloading, the unloading curve turns over towards a curve with stiffness when forces become close to zero. Reloading occurs along the unloading path until displacement reaches the previously maximum displacement value. Further loading follows again the initial loading curve. In the opposite load direction an identical behaviour with opposite signs is assumed.

4.2 Implementation The model is implemented into the finite element method software Abaqus by defining a user element (UEL). The UEL requires the definition of the element stiffness and the reaction forces at the end of each load increment. Input parameters from the simulations are the displacements between the ends of the element, which are fed into the UEL by Abaqus. Via the input file, the user provides parameters for the load-displacement curve. Internally, state variables are tracking the permanent deformations by saving the maximum relative displacement after each load increment. This allows securely identifying the current status, i.e. if loading happens along the first loading curve or as un- /reloading. For each displacement quantity, two state variables are used, which are used for positive and negative load directions independently. For each degree of freedom of the element, an independent definition of the curves and parameters is considered. Herein, only plane situations, i.e. relative displacements parallel and perpendicular to the element orientation and relative rotations within the plane, are taken into account. The model could be extended to a general load situation characterized by six degrees of freedom of the UEL. 5 MODEL VERIFICATION The models capabilities are demonstrated in three steps (as shown in Figure 2), where the transition from the embedment level to the global behaviour of connections within a structure is shown. The modelling approach is verified by comparison with experiments on these three structural levels. 5.1 Step 1: From embedment to single-dowel connection behaviour The embedment behaviour of dowels embedded into laminated veneer lumber (LVL; type Kerto S, Metsä Wood, Finland) was studied in a test series according to EN 383 [4]. The dowels had a diameter of 12 mm and showed high yield strength to avoid plastic deformations in the dowel [5]. Tests were performed for a variety of angles between the load and the grain direction. Figure 4 (top) shows the embedment stress over the dowel displacement for different load-to-grain directions. The behaviour is approximated by the regression function specified in Equation (1) using a sum of three exponential functions (see Table 1 for the coefficients). Table 1: Embedment parameters for a three-parameter model (according to Equation (1)) for a 12 mm dowel (values for in N/mm, for in mm -1 ) angle,,, 00 66.8 66.6 4.68-0.512-0.501-0.0146 45 56.1 5.10 55.1-0.576-0.00147-0.576 90 47.1 8.61 46.6 -.635-0.00315-0.637 The numerical model simulates a dowel-type steel-to- LVL connection with a 12 mm dowel applying a beam on non-linear embedment approach [1] using the connector elements described in Section 4. The properties for the dowel are well-known properties with the respective stress-strain diagram shown in Figure 4 (see also [5] for a more detailed description). Figure 4: Embedment behaviour for 0 (blue), 45 (green), and 90 (red) load-to-grain angles (top); stress-strain diagram for the steel dowel material (bottom) The modelling of the single-dowel connection follows the approach of a beam on non-linear elastic foundation [1]. Due to symmetry reasons, only one half of the single-dowel connection was modelled. The dowel was modelled by using quadratic beam elements (of type B32 in Abaqus Standard) and elasto-plastic material properties as documented in Figure 4. Spacing between the nodes was 1 mm. At the same positions as the dowel s nodes, additional nodes representing the LVL embedment of the connection were placed. Those were held hold rigid over the loading process. The non-linear UEL elements link the nodes on the dowel axis to the fictitious nodes representing the embedment into the LVL. The non-linear connection properties for the UEL were taken as shown in Table 1 and represent the embedment behaviour, while the lower unloading stiffness was set equal to 0.1 N/mm and considered to go back to the initial condition of zero load and zero displacement. Loading was applied displacement-controlled at the dowel in the symmetry plane of the connection by means of repeated loading-unloading displacement cycles with increasing amplitude. The comparison between the model predictions and the tests shows excellent agreement at low displacements below 2 mm, in the region of highest connection stiffness (see Figure 5). The stiff un-/reloading sections

are identical to the initial loading stiffness of the connection. At higher displacements, the model underestimates the resulting forces clearly. This point coincides with the full plastification of the dowel at the symmetry plane. The use of beam sections for the representation of the steel dowel with a diameter of 12 mm and with only 1 mm node spacing, at the same time with a plastic material behaviour, is obviously not very suitable. The dowel behaves too soft, is bending too easily and the counterforce cannot build up. Boundary and loading conditions (4-point bending with the supports at the inner triple points, the load application at the beams ends) are illustrated in Figure 6. Figure 6: Geometry of the test set-up [6] Figure 5: Load-displacement behaviour of single-dowel connections for 0 (blue), 45 (green), and 90 (red) load-tograin angles; experiments in dashed, simulations in solid lines The non-linear behaviour of the connections is nevertheless reproduced in terms of the trend, though the absolute values are underestimated. In accordance to the experiments, both on embedment and on connection level, the connections loaded under 0 shows highest stiffness and load level, the behaviour for loading at 90 lowest, respectively. The stiffness at higher displacements is highest for 90 in both experiment and model. 5.2 Step 2: From single- to multiple-dowel connections In this step, the behaviour of single-dowel connections at different load-to-grain angles is combined to give the combined connection behaviour for multi-dowel connections. In a recently finished research project on multi-dowel connections [6], tests on reinforced steel-to-lvl connections under pure bending moment were conducted. The basic geometry of the test set-up and the connection is shown in Figure 6, whereby in the experiments both, a circular and squared pattern, was used. In the example considered for model validation herein, a connection with nine dowels of 12 mm diameter, arranged in a square pattern with horizontal and vertical dowel spacing of 120 mm is used. The material properties of the LVL and the dowels are identical to properties used in Step 1 (see Section 5.1). The setup consists of a steel-to-lvl connection with a 10 mm steel plate and 12 mm dowels. The steel beam was formed by two steel U-profiles. The wood beam was made of LVL (Kerto S, Metsä Wood, Finland) with a rectangular cross-section of 114 x 480 mm 2 (two beams of 51 mm thickness with a 12 mm plate in between). The numerical model at this level considers the beam sections with the connection only. Hereby, the centre nodes act as master nodes for the wood beam and the steel plate, respectively. Distributing beam elements are attached at the master nodes on both sides, forming a star-like system. The distribution elements are considered quasi-rigid by assigning large cross sections and high stiffness properties. The non-linear UEL elements are connected at the ends of the distribution beams and represent the single-dowel connections. Each of the nine single-dowels is modelled by a single non-linear element. The properties for the elements are given in Table 2, whereby a three-parameter approximation according to Equation (1) was used. Since the load-to-grain angle in case of moment loading is known beforehand, the properties are assigned respectively for each dowel (top and bottom dowels at 0, left and right dowels at 90, and the corner dowels at 45 ; the centre dowel is unloaded in this configuration, the parameters for 0 were used). Table 2: Single-dowel parameters for a three-parameter model (according to Equation (1)) for a 12 mm dowel (values for in kn/m, in m -1 ) angle,,, 00 6900 298 4140-487 -.00316-487 45 4420 414 4830-572 -.00703-572 90 3860 679 3900-616 -0.000126-617 One of the master nodes is fixed with respect to horizontal and vertical displacement as well as with respect to rotation. On the other master node, the respective relative deformation is applied. In order to calculate the connection s behaviour, three different loads are applied, providing load-displacement curves for loading parallel and perpendicular to the beam (in this case equal to the grain orientation) as well as a moment-rotation diagram. Here, only the latter is validated since only moment loads were applied in the experiment [6]. Figure 7 shows the moment-rotation curves from the tests and the simulation. The simulation again captures the main features that characterize such a connection in rotation quite well. At small rotations, a rather stiff behaviour is observed. The stiffness decreases continuously until a rather linear behaviour is

encountered after approximately 0.03 rad. The un- and reloading runs parallel with the initial stiffness. However, the initial stiffness is underestimated in the model, having only approx. 50 % of the rotational stiffness of the experiment. The moment is therefore also underestimated, but the model prediction runs parallel at larger rotations. Table 3: Two-parameter model (according to Equation (1)) for a multi-dowel steel-to-lvl connection (values for in knm/rad, in rad -1 ) DOF,, rel. rotation 3240 308-190 -20.1 Figure 8 compares the reaction forces at the load introduction points (at the end of the beams). The beam model with a connection element predicts the experiment very well. Unloading stiffness is again running parallel to the initial stiffness. Figure 7: Comparison of moment-rotation curves from experiment (blue) and simulation (blue), stiffness in thin lines Differences between model calculations and experiments might indicate a homogenization effect or a stiffening effect in the multi-dowel connection. Alternatively, the quasi-elastic stiffness might be underestimated in singledowel connection tests. Another possible influence and a reason for the differences might be given in the preparation of the specimen, more precisely in the time lag between the drilling and the insertion of the steel dowels. A long time lag might lead to pre-stresses in the timber matrix when inserting a dowel in a smaller hole due to moisture changes induced swelling and a reduced hole diameters. 5.3 Step 3: From multi-dowel connections to the structural level The final step for use of the model is on the structural level. Hereby, the multi-dowel connection is further simplified and only load-displacement relationships for moment, normal and shear forces (abbreviated M, N, and V) are considered in the model. Hence three degrees of freedom are active, namely the relative displacements in parallel and transversal directions in relation to the wood grain orientation as well as the relative rotation. The connection behaviour, in terms of moment-relative rotation characteristics (see Figure 8), is now described by a two-parameter model using a curve-fitting process with Equation (1) as a regression function, in order to obtain an analytical curve as input to the model (parameters are documented in Table 3). A single nonlinear UEL element is therefore sufficient to describe the multi-dowel connection behaviour. The steel and wood beams are discretized by elements of 5 cm length using linear beam elements (of type B21 in Abaqus Standard). Properties regarding cross-section geometry and material properties are assigned respectively (see Section 5.2). No considerations regarding the steel plate are made. Figure 8: Comparison of the reaction forces at the load points 5.4 Model limitations By means of the validation steps, the possibilities and the agreement of the modelling approach to experiments could be shown. However, certain limitations became obvious as well. On the embedment level, the model uses a certain set of input parameters that coincide with the respective embedment behaviour for a certain dowel diameter and load-to-grain direction. At larger deformations with slender dowels (as in the example in Section 5.1) the dowel undergoes severe bending at the symmetry plane, due the formation of a plastic hinge. The simulation of such large rotations by means of the beam model is questionable and should be revisited. Better agreement with experimental data was found by modelling the steel dowel by means of a beam chain with rotational connectors that account for plastic deformations between beam segments [5]. Additionally, at large rotations the dowel heads are pulled into the bore-hole and the contact situation changes severely. This includes that a rope effect in the steel dowel is activated, acting along the dowel s axis due to frictional forces in the dowel-wood interface. This effect increases the load-bearing capacity and stiffness of the experiments, but is not accounted for in the simulation. Single-dowel connections were however tested with steel dowels that protruded over the wood surface, allowing for an increased contact area with increased bending deformations of the dowel. On the single-dowel connection level, the input parameters are the load-displacement curves for singledowel connections for specific load-to-grain angles. So far, the orientation for each dowel has to be known before-hand in order to provide the respective parameter set. The effect of the load-to-grain angle could be taken

into account by using an orientation dependent set of parameters, such as presented in [7]. The modelling approach for the multi-dowel connection does not account for interaction of internal forces. This is for instance the case in the combination of normal force with a bending moment, which leads to various load-tograin directions for each of the dowels that even change during the loading process. At the same time, the centre of rotation shifts accordingly. Extension of the model to consider load cases with combinations of internal forces, thus allowing for a priori unknown load-to-grain angles in the single dowels, would allow the model to be more adequate for engineering applications. 6 APPLICATIONS In a next step, the model is exploited in a study on the influence of certain parameters on the single-dowel connection behaviour, namely the side member thickness and the corresponding initial loading path as well as the unloading and reloading behaviour. Special emphasize is placed on the steel dowel deformation behaviour, which strongly affects the un-/reloading cycles. 6.1 Influence of side member thickness on singledowel connection behaviour The influence of the side member thickness on the loaddisplacement behaviour of a single-dowel connection is studied in the following. The connection is identical to the one presented in Step 1 (see Section 5.1) with 0 load-to-grain orientation. The length of the dowel is step-wise increased from 15 to 95 mm (in 10 mm steps). Hence the side member thickness increases from 9 to 89 mm in 10 mm steps as well. Not accounting for the above-mentioned limitations of the models, the basic failure modes of this type of double-shear timber-to-steel dowel connection according to Eurocode 5, Equation (8.11) [3] are clearly reproduced (see Figure 9 for the load-displacement curves and Figure 10 for the shape of the deformed dowels). Connections comprising dowels with low slenderness (9, 19, and 29 mm side member thickness) show continuous curves with clearly increasing stiffness at higher slenderness. The failure mode f (Equation (8.11) in Eurocode 5 [3]) shows no plastic dowel bending so that only the embedment behaviour characterizes the non-linearity. The embedment is hence approximately identical regarding embedment displacements and forces. Failure mode g (Equation (8.11) in the Eurocode 5 [3]) is characterized by a single plastic hinge in the middle plane of the connection. The dowel reaches maximum bending capacity and a clear difference in the embedment over the length of the dowel is visible. With longer dowels, the ends of the dowels get in contact with the opposite side and hence a counter-acting force builds up. The models limitations still prevent a realistic approximation of the load capacity. Clearly visible is the kink in the curves at a displacement of around 0.80 mm displacement when the plastic hinge forms, which appears localized in the first beam elements. No significant differences in stiffness are observed. Secondary plastic hinges form in failure mode h (Equation (8.11) in the Eurocode 5 [3]), as a reason of high-enough counter-acting forces at the dowels ends. Slightly higher loads can be applied but the load gains become smaller. Figure 9: Load-displacement curves for varying side member thickness Figure 10: Comparison of the deformed dowel shape (top, with von Mises stresses in colour) and embedment stress (bottom) distribution for varying side member thicknesses at a displacement of = 12 mm Figure 11 shows the design values according to the design rules provided in Eurocode 5 [3] in dependence of the side member thickness. The following values are assumed: = 120 Nm, = 12 mm, = 25 N/mm 2. Comparing the design values with the model, it becomes clear that connections of low slenderness (failure mode f) are well approximated by the model. Though the load levels are underestimated, also the distinction between failure modes g and h is well represented in the model. Figure 11: Connection forces according to Eurocode 5 [3] over varying embedment length, i.e. side member thickness 6.2 Envelope curves for cyclic loading In the following, the study is extended to account for cyclic loading with increased amplitude. The study is

again performed on a 12 mm dowel with LVL embedment. The cyclic loads are applied at +2/-2/+4/- 4/+8/-8/+16/-16 mm. Results are compared for dowel length of 15, 45, and 95 mm corresponding to side member thicknesses of 9, 39, and 89 mm, respectively, see Figure 12. The single-dowel connection with 9 mm side member thickness unloads linearly until close to zero force is reached and loads again with the opposite sign, hence exactly as illustrated in Figure 3. For the connection with a side member thickness of 29 mm, the dowel forms a plastic hinge in the centre and gets in contact with the surrounding wood on the ends. The unloading occurs stiff and linear but as soon as zero loads are reached, force in the opposite direction builds up (see Figure 12). The plastically bend dowel gets at this stage in contact at the ends with the wood in the opposite direction. Hence, it is not loaded along the full length, but the embedment stresses are gradually increasing. Once the dowel is bent back (elastically or plastically), contact is established along the full length so that the ordinary loading scenario occurs. If this is done repeatedly with higher amplitude, the hole is worn out and the unloading reaches again a stage of zero force. Figure 12: Envelope curves for connections under cyclic loading; dowel length 15 mm (blue), 45 mm (red), and 95 mm (green) Even longer dowels are always embedded into the wood. Hence there is a reaction force throughout the unloading cycles. Interestingly is that this force is lower (approx. 5 kn) than for the shorter dowel (approx. 9 kn). In this load scenario, the dowels are repeatedly bent back and forth in the plastic domain. In the model, the material behaves perfectly plastic, while fatigue and damage is not taken into account. Those are of course important design criteria limiting the capacity and possibilities of the connection in practical applications. 7 CONCLUSIONS A connector element able to account for highly nonlinear load-displacement relationships has been developed and presented in this contribution. Particular focus was laid on a suitable representation of permanent deformations, which occur in connections due to plasticity in the steel connector, but also in the wood due to embedment behaviour. Possible applications have been shown for dowel-type connections, from the embedment level up to the structural scale of connections. The developed numerical element can show its capabilities best on the embedment scale of a connector into wood. It allows e.g. to investigate the load distribution along the dowel also during unloading. With this feature, the consequences of repeated load and unloading cycles can be studied. This affects e.g. the formation of increasing clearance between the dowel and the bore-hole and the consequently minimized stiffness. For slender dowels, which form one or more plastic hinges during loading, limits for cyclic loading can be determined. Hence a clear separation between elastic and plastic dowel bending is provided by the model. Plastic material deformations, particularly under cyclic loading, may lead to fatigue failure. Deploying the single-dowel model to a multi-dowel connection will allow determining the unloading characteristics even at this level. REFERENCES [1] G. Hochreiner, T. K. Bader, K. de Borst, and J. Eberhardsteiner, Stiftförmige Verbindungsmittel im EC5 und baustatische Modellbildung mittels kommerzieller Statiksoftware, Bauingenieur, vol. 88, pp. 275 289, 2013. [2] M. Dorn, K. de Borst, and J. Eberhardsteiner, Experiments on dowel-type timber connections, Engineering Structures, vol. 47, pp. 67 80, 2012. [3] DIN EN 1995-1-1, Eurocode 5: Design of timber structures Part 1-1: General Common rules and rules for buildings, no. DIN EN 1995 1 1. DIN Deutsches Institut für Normung e. V., 2010. [4] DIN EN 383, Timber Structures Test methods Determination of embedment strength and foundation values for dowel type fasteners, no. DIN EN 383:2007. DIN Deutsches Institut für Normung e.v., 2007. [5] T. K. Bader, M. Schweigler, E. Serrano, M. Dorn, B. Enquist, and G. Hochreiner, Integrative experimental characterization and engineering modeling of single-dowel connections in LVL, Construction and Building Materials, vol. 107, pp. 235 246, 2016. [6] T. K. Bader, M. Schweigler, G. Hochreiner, E. Serrano, B. Enquist, and M. Dorn, Dowel deformations in multi-dowel LVL-connections under moment loading, Wood Material Science and Engineering, vol. 10, no. 3, pp. 216 231, 2015. [7] T. K. Bader, M. Schweigler, G. Hochreiner, and J. Eberhardsteiner, Load distribution in multi-dowel timber connections under moment loading integrative evaluation of multiscale experiments, in WCTE 2016, Vienna, Austria, 2016.