Numerical simulation of moisture driven fracture in mechanical timber connection using XFEM

Structural timber and glulam elements are an appealing alternative when it comes to choosing between structural elements as load bearing parts in e.g. halls, arenas and residential buildings. The wooden material is relatively strong in respect to its weight and its stiffness is sufficient enough to allow its use in a wide range of applications. However, there are also challenges associated with handling the material, one of which is the dimensional instability associated with moisture changes. The effect of climate variations on moisture induced deformations, stresses and failure in timber structures has already been addressed by several researchers, see e.g. [1] and [2]. A numerical model developed in the finite element package Abaqus is proposed herein to simulate crack propagation caused by variation in climate. In mechanical connections moisture induced strains in combination with boundary conditions that introduces constraints can lead to crack development and in turn weakening of wooden structures. Previous application of fracture mechanics typically focused on crack development caused by pure mechanical loading, see e.g. [3] for methods summarized and typical applications. Within the scope of the current work a numerical model is presented to simulate moisture driven crack growth within the beam/column dowel group connection shown in Figure 1. The model consists of two dimensional hygro-mechanical plane stress and XFEM analysis coupled to a nonlinear transient moisture flow analysis. A visualization of the considered problem is given in Figure 1. This figure shows a beam to column connection, which is exposed to natural climate variation (a). A schematic description of the problem is shown in Figure 1 (b). Figure 1 (c) shows simulated moisture content gradient and significant cracked beam because of the deformation constraints imposed by the dowels. The transient non-linear moisture flow was modelled using Fick’s law of orthotropic diffusion, using different diffusion coefficient in the two main directions, the length direction of the beam (assumed parallel to the fibers) and the direction perpendicular to that. The moisture transport in parallel direction was taken to be dominant. The shrinkage coefficients experience different values in perpendicular and parallel direction, αperp and αpar, respectively. For the fracture model, the critical energy release rate, GIC, is set to 300 J/m2, the strength in the perpendicular direction, ft,perp, to 2.5 MPa and the stiffness perpendicular and parallel to the length directions of the fibres are Eperp= 500 MPa and Epar= 10 000 MPa respectively