Multi-scale modelling of rolling shear failure in cross-laminated timber structures by homogenisation and cohesive zone models

In this paper we investigate the rolling shear failure in cross-laminated timber structures by homogenisation and cohesive zone models. In order to predict the structural response, four spatial scales are interlinked within a purely kinematic multi-scale modelling framework. The constitutive description has incorporated information coming from the wood cell-wall in the order of a few nanometres, wood fibres with dimensions of tens of micrometres and growth rings described by a few millimetres. The computational homogenisation scheme is solved sequentially from the lowest to the highest level in order to determine the effective mechanical properties for the fourth (structural) scale represented by a cross-laminated timber plate with dimensions of the order of one meter. In order to simulate the cracking in the material, a cohesive zone model is adopted at the homogenised macroscopic scale. The finite element problem is then solved using a mixed domain decomposition strategy due to its huge number of unknowns. This approach allows us to capture interlaminar and inter-fibre cracking and to solve the macroscopic equilibrium problem using parallel computations. Our numerical predictions are compared with experimental results and are validated successfully. In particular, we study the influence of wood density, edge-gluing and span-to-depth ratio on the rolling shear failure in cross-laminated timber.