ORTHOTROPIC YIELD CRITERIA IN A MATERIAL MODEL FOR TIMBER STRUCTURES

Authors

  • Leszek Małyszko University of Warmia and Mazury in Olsztyn

Keywords:

structural mechanics, timber structures, biaxial loading, orthotropic material, multi-surface plasticity, finite element method

Abstract

The continuum structural model for the failure analysis of timber structures in the plane stress state is discussed in the paper. Constitutive relations are established in the framework of the mathematical multi-surface elasto-pla-sticity theory with three orthotropic strength criteria that have been incorporated in the model as the plasticity conditions. The invariant form of the criteria is given based on the representation theory of scalar-valued functions of the orthotropic invariants. The model is implemented into a commercial finite element code by means of user-defined subroutines. Introductory implementation tests of the proposed numerical algorithm are presented in the paper.

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References

Boehler J.P. (Ed.) 1987, Applications of tensor functions in solid mechanics. CISM Courses and Lectures. No. 292, Springer-Verlag, Wien -New York.

Burzyński W. 1928, Studium nad Hipotezami Wytężenia, Nakładem Akademii Nauk Technicznych, Lwów, 1928, cf. also the English translation: Selected passages from Włodzimierz Burzyński 's doctoral dissertation „Study on Material Effort Hypotheses" printed in Polish by the Academy of Technical Sciences, Lwów, 1928, 1-192, Engineering Transactions, 57, 185-215, 2009.

DIANA User's manual Release 9.3, 2009, TNO DIANA BV.

Eberhardsteiner J. 2002, Mechanisches Verhalten von Fichtenholtz -Experimentelle Bestimmung der biaxialen Festigkeitseigenschaften. Springer, Vienna.

Geniev G.A. 1981, On a strength criterion of timber in a plane stress state. (in Russian). Stroitelna mechanika i rascet sooruzenii, 3, Moskva, pp. 15-20.

Geniev G.A., Kurbatov A.S., Samedov F.A. 1993, Problems of limit analysis and plasticity for anisotropic materials. (in Russian). Interbuk, Moskva.

Geniev G.A., Małyszko L. 2002, Selected strength and plasticity problems of anisotropic structural materials. Proc. Intern. IASS Symp. on LSCE, Obrębski J.B. (Ed.), Warsaw, vol. 1, pp. 309-316.

Hill R. 1948, A theory of the yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. London, A 193 (1948) 281-297.

Hoffman O. 1967, The brittle strength of orthotropic materials. J. Compos. Mater., 1, pp. 200-206.

Jemioło S., Małyszko L. 2008, New failure criteria for orthotropic materials. [in:] Monograph Computer systems aided science and engineering work in transport, mechanics and electrical engineering, Radom, Poland, pp. 223-228.

Mackenzie-Helnwein P., Eberhardsteiner J., Mang H.A. 2003, A multi-surface plasticity model for clear wood and its application to the finite element analysis of structural details. Computational Mechanics, 31, Springler Verlag, pp. 204-218.

Mackenzie-Helnwein P., Mullner H.W., Eberhardsteiner J., Mang H.A. 2005, Analysis of layered wooden shells using an orthotropic elastoplastic model for multi-axial loading of clear spruce wood. Comput. Methods Appl. Mech. Engrg., 194, Elsevier, pp. 2661-2685.

Małyszko L., Jemioło S., Bilko P. 2010, Implementation tests of orthotropic elastic-plastic models into a commercial finite element code. Proc. XVI Intern. Sem. of IASS Polish Chapter on LSCE, Obrębski J.B. (Ed.), Warsaw, pp. 51-56.

Małyszko L., Jemioło S., Gajewski M., Bilko P. 2009, FEM and Constitutive Modelling in Failure Analyses of Masonry Structures. Orthotropic Failure Criteria. WTA-Schriftenreihe, Heft 33, Leuven, Belgium, pp. 371-394.

Mises R. 1928, Mechanik der plastischen Formanderung von Kristallen. ZAMM, vol. 8, No. 3, 161-185.

Olszak W., Urbanowski W. 1956, The plastic potential and the generalized distortion energy in the theory of non homogeneous anisotropic elastic-plastic bodies. Arch., Mech. Stos., 8, 671-694.

Rychlewski J. 1984, Elastic energy decomposition and limit criteria. Published originally in Russian in Advances in Mechanics, 7, 51-80, 1984 and republished recently in English translation in Engineering Transactions, 59, 31-63, 2011.

Simo J.C., Hughes T.J.R. 1998, Computational Inelasticity. Interdisciplinary Applied Mathematics, Springer.

Schmidt J., Kaliske M. 2009, Models for numerical analysis of Wooden structures. Engineering Structures, 31, Elsevier, pp. 571-579.

Szeptyński P. 2011, Some remarks on Burzynski's failure criterion for ani-sotropic materials. Engineering Transactions, 59, pp. 119-136.

Tsai S.W., Wu E.M. 1971, A general theory of strength for anisotropic materials. J. Compos. Mater., 5, pp. 58-80.

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Published

2011-12-19

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