Lattice Models for the Prediction of Load-Induced Failure and Damage in Wood


  • William G. Davids
  • Eric N. Landis
  • Svetlana Vasic


Strain softening, lattice models, crack bridging, fracture, finite element analysis


Lattice models, which are essentially networks of springs having variable strength and stiffness, are used to predict the response of structural softwood to various mechanical loadings. The use of lattice models is motivated by the desire to mimic the morphology of wood, and thus realistically predict both load-displacement response and experimentally observed damage patterns that are not well captured by conventional continuum-based models. The goal of the work described in this paper was to evaluate suitability of lattice models for predicting several different failure modes of structural softwood, and to establish a methodology for matching model parameters to measured material properties. Using least squares techniques, the lattice model member properties were determined to give optimal predictions of bulk elastic constants and expected load-displacement response to failure under perpendicular-to-grain tension, parallel-to-grain tension, and shear. The lattice models were shown to accurately capture load-displacement response, including experimentally observed strain softening under perpendicular-to-grain tension. In addition, the lattice models successfully predicted damage localization, including crack bridging and microcracking around the critical crack. Mesh size effects were also examined, and while the lattice models are dependent on mesh size, it is demonstrated that for a fixed cell aspect ratio, a simple scaling of the lattice model strength and stiffness properties to account for cell size can yield reasonable predictions of ultimate capacity.


Au, T., and P. Christiano. 1993. Fundamentals of structural analysis. Prentice Hall, Inc., Englewood Cliffs, NJ.nBodig, J., and J. R. Goodman. 1973. Prediction of elastic parameters for wood. Wood Science 5(4):249-264.nBodig, J., and B. Jayne. 1993. Mechanics of wood and wood composites. Krieger Publishing Co., Malabar, FL.nCowin, S. C. 1979. On the strength and anisotropy of bone and wood. Trans. ASME 46:832-838.nCramer, S. M., and J. R. Goodman. 1983. Model for stress analysis and strength prediction of lumber. Wood Fiber Sci. 15:118-149.nCramer, S. M., and J. R. Goodman. 1986. Failure modeling: A basis for the strength prediction of lumber. Wood Fiber Sci. 18:446-459.nCramer, S. M., and W. Forhell. 1990. Method for simulating tension performance of lumber members. J. Struct. Eng. 116:2729-2746.nCurtin, W., and H. Scher. 1990. Brittle fracture of disordered materials: A spring network model. J. Mater. Res. 5(3):535-553.nDavids, W. G., and G. M. Turkiyyah. 1999. Multigrid preconditioner for unstructured nonlinear 3D FE models. J. Eng Mech. 125:186-196.nHankinson, R. L. 1921. Investigation of crushing strength of spruce at varying angles of grain. Air Service Information Circular No. 259, U.S. Air Service.nHibbeler, R. C. 1990. Structural analysis. Macmillan Publishing Company, New York, NY.nIllston, J. M., ed. 1994. Construction materials: Their nature and behaviour. E &FN Spon, London, UK.nJirásek, M., and Z. Baźant. 1995. Macroscopic fracture characteristics of random particle systems. Int. J. Fracture 69:201-228.nRaghuprasad, B., D. Bhat, D., and G. Bhattacharya. 1998. Simulation of fracture in a quasi-brittle material in direct tension—a lattice model. Eng. Fracture Mech. 61:445-460.nSchlangen, E., and E. Garboczi. 1996. New method for simulating fracture using an elastically uniform random geometry lattice. Int. J. Eng. Science 34(10):1131-1144.nSchlangen, E., and E. Garboczi. 19997. Fracture simulations of concrete using lattice models: computational aspects. Eng. Fracture Mech. 57(2/3):319-332.n"Using Matlab." The Mathworks, Inc., Natick, MA, 1998.nVasic, S. 2000. Applications of fracture mechanics to wood. Ph.D. thesis, University of New Brunswick, Fredericton, Canada.nVasic, S., and I. Smith. 1996. The brittleness of wood in tension perpendicular to the grain: Micromechanical aspects. Pages 818-820. In Proc. World Conf. Timber Engineering, COST 508, Stuttgart, Germany.nVasic, S., I. Smith., and E. Landis. 2001. Fracture zone characterization—Micro-mechanical study. Wood Fiber Sci. (in press).nWood Handbook. Forest Products Laboratory Report No. FPL-GTR-113. Madison, WI, 1999.n






Research Contributions