General shell section properties and failure model for cross-laminated timber obtained by numerical homogenization

In this study homogenized mechanical properties are derived for structural finite element analysis of cross-laminated timber (CLT) discretized by means of shell elements. In the first step, based on the results of experimental three-point bending tests on a CLT slab component, a numerical optimization procedure is applied to identify the elastic and plastic properties of the individual spruce wood laminates, considering orthotropic elasticity and Hill's yield criterion. Taking into account its periodic structure, a repeating unit cell (RUC) of the CLT is defined in the subsequent step. To this RUC specific loading conditions are imposed successively, yielding the entries of the homogenized elastic stiffness matrix of a general shell section. Extending the RUC simulations into the inelastic domain of deformation results in a homogenized failure surface on the structural scale, which is implemented as a postprocessing variable in a commercial finite element program. Throughout all analyses, in sensitivity studies the most decisive material properties are identified. Results of comparative simulations on a homogenized structural model and an elaborate full three-dimensional finite element model of a point-supported CLT slab show the accuracy and efficiency of the proposed approach based on homogenized mechanical properties.