Development and experimental validation of a continuum micromechanics model for the elasticity of wood

This contribution covers the development and validation of a microelastic model for wood, based on a four-step homogenization scheme. At a length scale of several tens of nanometers, hemicellulose, lignin, and water are intimately mixed, and build up a polymer (polycrystal-type) network. At a length scale of around one micron, fiberlike aggregates of crystalline and amorphous cellulose are embedded in an contiguous polymer matrix, constituting the so-called cell wall material. At a length scale of about one hundred microns, the material softwood is defined, comprising cylindrical pores (lumen) in the cell wall material of the preceding homogenization step. Finally, at a length scale of several millimeters, hardwood comprises larger cylindrical pores (vessels) embedded in the softwood-type material homogenized before. Model validation rests on statistically and physically independent experiments: The macroscopic stiffness values (of hardwood or softwood) predicted by the micromechanical model on the basis of tissue-independent (‘universal’) phase stiffness properties of hemicellulose, amorphous cellulose, crystalline cellulose, lignin, and water (experimental set I) for tissue-specific composition data (experimental set IIb) are compared to corresponding experimentally determined tissue-specific stiffness values (experimental set IIa).

[1]  R. Newman,et al.  Determination of the Degree of Cellulose Crystallinity in Wood by Carbon-13 Nuclear Magnetic Resonance Spectroscopy , 1990 .

[2]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[3]  Christian Hellmich,et al.  Shotcrete elasticity revisited in the framework of continuum micromechanics : From submicron to meter level , 2005 .

[4]  L. Salmén,et al.  Cell wall properties and their effects on the mechanical properties of fibers , 2002 .

[5]  A. Stamm.  Calculations of the void volume in wood , 1938 .

[6]  A. Zaoui.  Continuum Micromechanics: Survey , 2002 .

[7]  J. Vincent,et al.  From cellulose to cell. , 1999, The Journal of experimental biology.

[8]  J. Minor,et al.  Further Studies on Elastic Properties of Douglas Fir , 1989 .

[9]  David E. Kretschmann,et al.  Modeling Moisture Content-Mechanical Property Relationships For Clear Southern Pine , 2007 .

[10]  R. Armstrong,et al.  Young's modulus of lignin from a continuous indentation test , 1975 .

[11]  W. Cousins.  Elastic modulus of lignin as related to moisture content , 1976, Wood Science and Technology.

[12]  D. Grosser,et al.  Chemische Zusammensetzung von Nadel- und Laubhölzern , 2013, Holz als Roh- und Werkstoff.

[13]  Christian Hellmich,et al.  Drained and Undrained Poroelastic Properties of Healthy and Pathological Bone: A Poro-Micromechanical Investigation , 2005 .

[14]  Christian Hellmich,et al.  Can the diverse elastic properties of trabecular and cortical bone be attributed to only a few tissue-independent phase properties and their interactions? , 2004, Biomechanics and modeling in mechanobiology.

[15]  A. Stamm.  The bonding force of cellulosic materials for water (from specific volume and thermal data) , 1937 .

[16]  E. Mayr.  This Is Biology: The Science of the Living World , 1997 .

[17]  J. Achenbach.  Wave propagation in elastic solids , 1962 .

[18]  Jozsef Bodig,et al.  Orthotropic Elastic Properties of Wood , 1970 .

[19]  Christian Hellmich,et al.  Micromechanical Model for Ultrastructural Stiffness of Mineralized Tissues , 2002 .

[20]  E. Sjöström,et al.  Wood Chemistry: Fundamentals and Applications , 1981 .

[21]  F. Kollmann,et al.  Dynamische Messung der elastischen Holzeigenschaften und der Dämpfung Ein Beitrag zur zerstörungsfreien Werkstoffprüfung , 1960, Holz als Roh- und Werkstoff.

[22]  Christian Hellmich,et al.  Mineral–collagen interactions in elasticity of bone ultrastructure – a continuum micromechanics approach , 2004 .

[23]  Michael F. Ashby,et al.  The mechanical properties of natural materials. I. Material property charts , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[24]  Masamichi Kobayashi,et al.  THEORETICAL EVALUATION OF THREE-DIMENSIONAL ELASTIC CONSTANTS OF NATIVE AND REGENERATED CELLULOSES : ROLE OF HYDROGEN BONDS , 1991 .

[25]  Karl J. Niklas,et al.  Plant Biomechanics: An Engineering Approach to Plant Form and Function , 1993 .

[26]  A. Sliker.  Measuring Poisson's ratios in wood , 1972 .

[27]  V. Bucur,et al.  Elastic constants for wood by an ultrasonic method , 1984, Wood Science and Technology.

[28]  J. Morrell,et al.  Marine wood chafing: An illustrated comment , 1985 .

[29]  J. Gril,et al.  Origin of the biomechanical properties of wood related to the fine structure of the multi-layered cell wall. , 2002, Journal of biomechanical engineering.

[30]  C. Skaar.  Wood-Water Relations , 1988, Springer Series in Wood Science.

[31]  L. Salmén,et al.  Variations in Transverse Fibre Wall Properties: Relations Between Elastic Properties and Structure , 2000 .

[32]  Jozsef Bodig,et al.  Mechanics of Wood and Wood Composites , 1982 .

[33]  R. Young,et al.  Introduction to Polymers , 1983 .

[34]  H. Carrington,et al.  CV. The elastic constants of spruce , 1923 .

[35]  J. Háfren,et al.  Changes in Cell Wall Architecture of Differentiating Tracheids of Pinus thunbergii during Lignification , 1999 .

[36]  Roger M. Rowell,et al.  The Chemistry of solid wood , 1984 .

[37]  W. Cousins.  Young's modulus of hemicellulose as related to moisture content , 1978, Wood Science and Technology.

[38]  A. C. O'sullivan.  Cellulose: the structure slowly unravels , 1997, Cellulose.

[39]  D. Fengel,et al.  Wood: Chemistry, Ultrastructure, Reactions , 1983 .

[40]  N. Laws,et al.  The determination of stress and strain concentrations at an ellipsoidal inclusion in an anisotropic material , 1977 .

[41]  M. Ashby,et al.  Cellular solids: Structure & properties , 1988 .

[42]  P. Perré,et al.  Microscopic tensile tests in the transverse plane of earlywood and latewood parts of spruce , 2000, Wood Science and Technology.

[43]  Michael F. Ashby,et al.  On the mechanics of balsa and other woods , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[44]  H. Hörig,et al.  Anwendung der Elastizitätstheorie anisotroper Körper auf Messungen an Holz , 1935 .

[45]  Luc Dormieux,et al.  Micromechanics of saturated and unsaturated porous media , 2002 .

[46]  Peter Fratzl,et al.  Cellulose and collagen: from fibres to tissues , 2003 .

[47]  R. Hearmon,et al.  Elasticity of Wood and Plywood , 1948, Nature.

[48]  Alfred J. Stamm,et al.  Wood and Cellulose Science , 1964 .

[49]  Stephen J. Eichhorn,et al.  The Young's modulus of a microcrystalline cellulose , 2001 .

[50]  Franz-Josef Ulm,et al.  A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials , 2003 .