Numerical modelling of dowelled connections in Laminated Veneer Lumber

The complex mechanical behaviour of timber makes it hard to predict the failure modes in connections made of timber in Finite Element Models (FEM). The combination of various failure modes (brittle and ductile) , anisotropic behaviour, contact of steel elements and large deformations that can occur in a timber joint challenges the use of FEM. To this date no widely used approach is available for the modelling of timber connections. This knowledge gap impedes the use of large timber connections for high rise buildings in seismic regions like New Zealand. For tall seismic resilient structures a profound understanding of the various failure modes of a connection is needed to guarantee a safe design. In this thesis a new model approach with the use of cohesive elements to simulate cracking is investigated for the prediction of the mechanical behaviour of connections. An embedment test simulation is a logical step towards this connection model. Timber can be characterised by its strong longitudinal fibres and the lignin that forms the bonding between the fibres. This anisotropic structure of the material results in a strong and stiff parallel and a weaker perpendicular behaviour of the material. Timber reacts ductile to compression loading and brittle in tension and shear loading. A typical crushing action of the timber (with micro cracking and densification of the timber) occurs when the maximum compression parallel to the grain stress is reached. The specific manufacturing process of Laminated Veneer Lumber (LVL) reduces the inhomogeneous character of timber. This improves the strength and the predictability of the material. The cracks that occur in tension and shear can cause four different brittle failure modes in a dowelled connection (row shear, group tear out, failure of the net cross section and tensile splitting). A brittle failure mode can be prevented when minimum end or edge distances and spacing between fasteners are satisfied. In that case a ductile failure is expected with plastic deformation of the dowel and crushing of the timber underneath the dowel. FEM is a powerful tool that is able to solve complex partial differential equation problems. Its basis lies in the linear formulation of small elements that are linked by coinciding nodal degrees of freedom to form a structure. The linear formulation has limited validity and a failure criteria is needed to define the onset of nonlinear behaviour. Multiple nonlinear approaches are available to accurately simulate the complex behaviour of timber in connections. The most promising approach is the use of cohesive elements at the locations where cracks are expected. The anisotropic nature of wood makes the prediction of crack locations in connections possible. The cohesive elements have a damage formulation to simulate strength and stiffness loss after the material strength is reached. This softening model hinders the solution procedure and therefore special solution techniques (e.g. line search, automatic stabilization and viscous regularization) are employed. A first model is made to simulate the embedment behaviour in LVL. In the embedment tests conducted by Franke and Quenneville a steel dowel is pushed in a timber block with a pre-drilled hole. In the translation of this test to an accurate FEM model three nonlinear phenomena are simulated (cracking, crushing in compression and contact). The cracking behaviour in tension and shear is modelled with cohesive elements with a damage formulation. These cracks are inserted at the location of potential crack growth. The remaining timber has a trilinear isotropic plastic hardening formulation to accurately predict the deformations in the LVL under compression loading. The last nonlinear phenomena is contact between the steel and the timber. This is simulated as "hard" contact in normal direction and frictional contact in tangential direction. The implicit solver encountered difficulties in converging due to contact alterations (chatter) and the softening behaviour in the cohesive elements. The automatic time incrementation algorithm reduced the increment size to overcome these difficulties. The analysis resulted in a load displacement curve that had good agreement with the experimental curve. A parameter study proved that the small difference can be related to the natural variation of material properties. The approach of the embedment FEM was implemented in a more complex connection model. The connection tests conducted by Ottenhaus et al. that is simulated consists of 4 dowels that connect two outer LVL blocks with an inner steel plate. The spacing was chosen in such a way that a ductile failure mode was expected with brittle failure modes at large deformations. In the connection model plasticity in the steel dowels, the size of the specimens and the inclusion of tension parallel cracks increased the complexity of the model. This increased the convergence difficulties and the analysis ceased (at 0.43 mm) before the maximum load was reached . A study was made to improve the stability of the numerical solution procedure. The impact of changing the formulations of cohesive elements, contact and the solution procedure on the convergence is tested. The viscous regularization and the initial dummy stiffness of the cohesive elements had the most influence on the convergence. With increased viscous regularization the implicit solver becomes more stable and computes more displacement increments (up to 6.91 mm). However, viscous regularization introduces artificial forces that significantly decreased the damage evolution. This prevented the formation of brittle failure mechanism. By reducing the initial dummy stiffness of the cohesive elements (down to 2 times the timber element stiffness) the convergence improved significantly. With this initial cohesive stiffness the global softening behaviour (up to 10.08 mm) and failure development that are observed in the experiments could be simulated. The failure development consisted of the formation of plastic hinges in the dowels, tensile splitting and finally row shear failure that completely removed the supporting action of the timber under the dowels. The decrease of cohesive element stiffness has impact on the effective stiffness of the adjacent timber elements and decreases the accuracy of the model. The model needs to be improved to make the predictions of the brittle failure development more accurate. With arc-length control, an explicit solver or the sequential linear analysis method the convergence might be increased, without the accuracy loss that is attributed to cohesive stiffness decrease. Further research is needed to improve this connection model approach.