Benjamin GIGER

Material modeling of cross-laminated timber by means of FEM

Every year timber as construction element becomes more important because wood is a biodegradable sustainable building material that also contributes to a pleasant room climate. The area of application of lumber is constantly expanded, however, there is still a lack on reliable technological foundations for this building material. This master thesis examines the mechanical properties of cross-laminated timber made of spruce wood. In a first step, static three-point bending tests on cross-laminated timber plates composed differently arranged wood laminates are performed. Based on a finite element model of the test objects, a numerical optimization procedure is applied to identify the material parameters such that the numerical load-displacement curve matches the experimental counterpart. In this respect, the elastic and plastic material parameters are separately optimized. The plastic behavior is described by means of Hill‘s criterion. This criterion is capable of reproducing the orthotropic strength values of lumber. Once the local material properties have been determined, two different homogenization procedures are applied based on the laminate plate theory respectively on a repeating unit cell. The result is the homogenized plate-shell stiffness matrix applicable to thin shells. Since, however, the considered cross-laminated timber elements behave more as a moderately thick shell, also the transverse shear stresses are identified. The outcomes of the homogenization procedures are validated, analyzing a point-supported slab utilizing a volume model and a corresponding shell model. In particular, the natural frequencies are used as an indicator of the stiffness distribution. It is shown that the plate and shell stiffness matrix of the repeating unit cell modeled shell and of the volume element are in an excellent agreement. Subsequently, the unit cell homogenization is extended into the inelastic domain. A failure surface is identified and implemented into a finite element code as post-processing variable. This variable is used to estimate the domains of plastic strains. Application to the slab in its ultimate limit state shows that the estimated plastic domains of the shell model are close to the ones of the volume model.