Published

2011-01-01

Two-dimensional wood drying stress simulation using control-volume mixed finite element methods (CVFEM)

Simulación bidimensional de esfuerzos de secado en la madera usando CVFEM

Keywords:

simulation, drying, wood, stress, creep, CVFEM. (en)
simulación, secado, madera, esfuerzos, creep, CVFEM. (es)

Authors

  • Carlos Salinas Universidad del Bio-Bio
  • Cristian Chavez Universidad del Bio-Bio
  • Yerko Gatica Universidad del Bio-Bio
  • Rubén Ananias Universidad del Bio-Bioa

The work was aimed at simulating two-dimensional wood drying stress using the control-volume finite element method (CVFEM). Stress/strain was modeled by moisture content gradients regarding shrinkage and mechanical sorption in a cross-section of wood. CVFEM was implemented with triangular finite elements and lineal interpolation of the independent variable which were programmed in Fortran 90 language. The model was validated by contrasting results with similar ones available in the specialised literature. The present model's results came from isothermal (20ºC) drying of quaking aspen (Populus tremuloides): two-dimensional distribution of stress/strain and water content, 40, 80, 130, 190 and 260 hour drying time and evolution of normal stress ( -2,5<σxx<1,2, MPa), from the interior to the exterior of wood.

El objetivo de este trabajo es el de simular esfuerzos bidimensionales de secado usando el método de volúmenes de control conformado por elementos finitos (CVFEM). Se modelan esfuerzos de secado en una sección transversal de madera sólida, producidos por gradientes de humedad asociados a los fenómenos de contracción y sorción mecánica. En particular, se implementa CVFEM con elementos finitos triangulares, interpolación lineal de la variable independiente al interior de él y programado en lenguaje Fortran 90. El modelo se valida contrastando resultados con trabajos similares disponibles en la literatura especializada. Finalmente, se muestran resultados originales de la modelación aplicada al secado isotérmico (20 ºC) de madera sólida de álamo (Populus tremuloides): distribución bidimensional de esfuerzo/deformación y contenidos de humedad para tiempos de secado igual a 40, 80, 130, 190 y 260 (h) y evolución transitoria de esfuerzos normales ( -2,5<σxx<1.2, MPa), desde el centro a la superficie de la madera.

References

Baliga B. R., Patankar S. V., A new finite element formulation for convection diffusion problems., Numerical Heat Transfer, Vol. 3, 1980, pp. 393-409.

Boley B. A., Weiner J. H, Theory of Thermal Stresses., John Wiley and Sons, Inc., New York, 1960.

Chen G, Keey, R.B, Walker J.F.C., The drying stress and check development on high-temperature kiln seasoning of sapwood Pinus radiate boards., Holz als Roh-und Werkstoff, Vol. 55, Nº 2, 1997, pp. 59-64.

Cheng, W., Morooka, T., Wu, Q., Liu, Y., Characterization of tangential shrinkage stresses of wood during drying under heated steam above 100 ºC., Forest Prod. J, Vol. 57, Nº 11, 2007, pp. 39-43.

Cloutier, A., Fortin, Y., Dhatt, G., A wood drying finite element model based on the water potential concept., Drying Technology, Vol. 10, No. 5: 1992, pp. 1151-1181.

Cloutier A., Fortin Y., Wood drying modeling based on the water potential concept: Effect of the hysteresis in the M-y relationship, Drying Tech., Vol. 12, Nº 8, 1994, pp. 1793-1814.

Ferguson, W.J., A control volume finite element numerical solution of creep problems., Int. J. Num. Meth. Eng, Vol. 40, No. 18, 1997, pp. 3463-3475

Ferguson, W.J., A numerical prediction of the effect of airflow and wet bulb temperature on the stress development during convective wood drying., In mathematical modeling and numerical techniques in drying technology, Ed. I. Turner, A.S. Mujumdar, 1997, pp. 259-277.

Ferguson, W. J., The control volume finite element numerical solution technique applied to creep in softwoods., Int. J. Solid Structures, Vol. 35, No. 13, 1998, pp.1325-1338.

Kang, W., Lee, N., Jung, H., Simple analytical methods to predict one-and two-dimensional drying stresses and deformations in lumber., Wood Sci. Technol., Vol. 38, Nº 6, 2004, pp. 417- 428.

Keey, R., Langrish, T., Walker, J., Kiln-drying of lumber., Springer-verlag, N.Y. 2000.

Keunecke, D.S.H, Niemz, P., Three-dimensional elastic behaviour of common yew and Norway spruce., Wood Science and Technology, Vol. 42, Nº 8, 2008, pp. 633-647.

McMillen, J., Stresses in wood during drying., Res. Rap. 1652 USDA Forest Service. Forest Products Lab. Madison, WI., 1963.

Martensson, A., Stevensson, S., Application of a material model describing drying stresses in Word., 5th IUFRO International wood drying conference, 1996, pp. 93-102.

Ormarsson, S., Cown, D., Dahlblom, O., Finite element simulations de moisture related distortion in laminated timber products of Norway spruce and radiata pine., 8th IUFRO International wood drying conference, 2003, pp. 27-33.

Pang, S., Mathematical modeling of kiln drying of softwood timber: Model development, validation and practical application., Drying Technology, Vol. 25, 2007, pp. 421-431.

Perre, P., Moser M., Matin, M., Advances in transport phenomena during convective drying with superheated steam and moist air., Int. J. Heat and Mass Transfer, Vol 36, Nº. 11, 1993, pp. 2725-2746.

Perre P., Turner, I., Determination of the material property variations across the growth ring of softwood for use in a heterogeneous drying model., Holzforschung, Vol. 55, Nº. 4, 2001, pp. 417-425.

Remond, R., Passard, J., Perre, P., The effect of temperature and moisture content on the mechanical behaviours of wood: a compressive model applied to drying and bending., European Journal of Mechanical Solid, Vol. 26, 2006, pp 558- 575.

Salinas, C., Ananias, R. A., Alvear, M., Simulación del secado convencional de la madera., Maderas Ciencia y Tecnología, Vol. 6, Nº. 1, 2004, pp. 3-18.

Salinas, C., Chávez, C., Gatica, Y., Ananias, R., Simulación del secado convencional de madera usando CVFEM., Revista Técnica de Ingeniería, Universidad de Zulia, vol. 34. Nº1, abril 2011.

Stevensson, S., Martensson, A., Simulation of drying stresses in wood Part III Convective air drying of sawn timber., Holz Roh Werkst, Vol. 60, 2002, pp. 72-80.

Thuvander, F., Kifetew, G., Berglund, L.A., Modeling of cell wall drying stresses in wood., Wood Sci. Technol., Vol. 36, 2002, pp.241-254.

Turner, I.W., Ferguson, W., An unstructured mesh cell-centered control volume method for simulating heat and mass transfer in porous media: Application to softwood drying, part I: The isotropic model., Appl. Math. Modeling, Vol. 19, 1995a, pp. 654-667.

Turner, I.W., Ferguson W., An unstructured mesh cell-centered control volume method for simulating heat and mass transfer in porous media: Application to softwood drying. Part II. The anisotropic model., Appl. Math. Modeling, Vol. 20, 1995b, pp. 669-674.

Turner, I., Mujumdar, A.S., Mathematical modeling and numerical techniques in drying technology., Marcel Dekker Inc., New York, ISBN 0-8247-9818-X, 1997, pp. 1-20.

USDA., Wood Handbook: Wood as un engineering material., report: FPL-GTR-190, 2010.

Young, R. The perpendicular to grain mechanical properties of red oak as related to temperature, moisture content and time., USDA, FPL-2079, Madison, USA,1957.

Zienkiewicz, O.C., Taylor R.L., The Finite Element Method., Fifth edition, published by Butterworth-Heinemann, Vol. 2. Solid Mechanics, 2000, pp. 365.

How to Cite

Two-dimensional wood drying stress simulation using control-volume mixed finite element methods (CVFEM). (2011). Ingeniería E Investigación, 31(1), 171-183. https://doi.org/10.15446/ing.investig.v31n1.20545