Collapse response of two-dimensional cellular solids by plasticity and cracking: application to wood

The competition between fracture and plasticity in periodic hexagonal honeycomb structures subjected to (i) intercell cracking, (ii) intrawall cracking and (iii) transwall cracking is examined, and their effect upon the macroscopic collapse response is explored using dedicated FEM analyses of unit cell configurations. These three cracking mechanisms are regularly observed in wood microstructures, and insight into their influence on the macroscopic collapse behavior is necessary for adequately designing timber structures against failure. The numerical results are presented by means of collapse contours in the hydrostatic-deviatoric stress space, illustrating the effects of wall slenderness, relative fracture (versus yield) strength, and the relative size of the plastic zone at the crack tip. Both the hydrostatic and deviatoric collapse strengths of the honeycomb strongly increase in the transition from brittle cell walls with low relative fracture strength to ductile cell walls with high relative fracture strength. This strength increase typically changes the shape of the collapse contour, and is the largest for transwall cracking, followed by intercell cracking and finally intrawall cracking. The ultimate collapse strength of the honeycomb is significantly more sensitive to the fracture strength than to the fracture toughness of the cell walls, and correctly approaches the plastic yield surface under increasing relative fracture strength. The numerical results may serve as a useful guideline in the experimental calibration of the local fracture and yield strengths of cell walls in wood.