an orthotropic continuum model for the analysis of masonry structures

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46 1995 TNO-95-NM-R07126. CONCLUSIONSAn anisotropic plane stress continuum model for the analysis of masonry structures has been presented.The model combines orthotropic elasticity with orthotropic plasticity. A composite yieldsurface that includes a Hill type yield criterion for compression and a Rankine type yield criterionfor tension has been developed. The model is novel in the sense that a relatively simple compositeyield surface is proposed and hardening and softening are included in a rational way. Modern plasticityconcepts as unconditionally stable implicit Euler backward return mappings, local Newton-Raphson iterative procedures and consistent tangent operators are used for all the modes of themodel. The performance of the implementation is assessed by means of single element tests. It isshown that the numerical algorithm is robust and numerically efÞcient.The model predicts different yield strengths and fracture energies along the material axes, both intension and compression. These features deÞne an extremely ßexible model capable of accommodatingthe behaviour obtained from experiments. The behaviour of the model is detailed by meansof single element tests, in which the response is evaluated upon different choices of the materialparameters. Unfortunately the number of test results of the composite material is relatively scarceand almost non-existent in the post-peak regime. The setup of experimental programs coordinatedby experimentalists and analysts seem therefore crucial.A comparison between numerical results and experimental results available is also included. Previousattempts to use macro-models, speciÞcally developed for masonry structures, included interfaceelements at the boundaries. The interface elements were responsible for most of the non-linear phenomenaobserved and, thus, only a poor validation of previously proposed macro-models exists. Itis shown that the model proposed in the present report is able to predict well the behaviour ofmasonry structures, with both ductile and brittle failure modes, as well as sufÞciently accurate collapseload values. However, this statement is only true if the structure is sufÞciently large that amacro-modelling strategy can be applied.
TNO-95-NM-R0712 1995 477. REFERENCESde Borst, R., The zero-normal stress condition in plane-stress and shell elasto-plasticity, Comm. in.Appl. Numer. Methods, Vol. 7, pp. 29-33 (1991)de Borst, R. and Feenstra, P.H., Studies in anisotropic plasticity with reference to the Hill criterion,Int. J. Numer. Meth. Engrg., Vol.29, pp. 315-336 (1990)Baºant, Z.P. and Oh, B.H., Crack band theory for fracture of concrete, Materials and Structures,RILEM, Vol. 93(16), pp. 155-177 (1983)CrisÞeld, M.A., Accelerated solution techniques and concrete cracking, Comp. Meth. Appl. Mech.Engrg., Vol. 33, pp. 585-607 (1982)Dhanasekar, M., Kleeman, P.W. and Page, A.W., Biaxial stress-strain relations for brick masonry, J.Struc. Engrg., Vol. 111(5), pp. 1085-1100 (1985)Dhanasekar, M. and Page, A.W., The inßuence of brick masonry inÞll properties on the behaviourof inÞlled frames, Proc. Intsn. Civ. Engrs., Part 2, Vol.81, pp. 593-605 (1986)Feenstra, P.H., Computational aspects of biaxial stress in plain and reinforced concrete, Dissertation,Delft University of Technology, Delft, The Netherlands (1993)Ganz, H.-R., Failure criteria for masonry, 5 th Canadian Masonry Symposium, Vancouver, Canada,pp. 65-77 (1989)Ganz, H.-R. and ThŸrlimann, B., Experiments about the strength of biaxially loaded masonry panels,Report 7502-3, Institute of Structural Engineering, ETH Zurich, Switzerland (in German)(1982)Ganz, H.-R. and ThŸrlimann, B., Experiments of masonry walls under normal and shear loading,Report 7502-4, Institute of Structural Engineering, ETH Zurich, Switzerland (in German) (1984)Hill, R., A theory of the yielding and plastic ßow of anisotropic metals, Proc. Roy. Soc. (London)A, Vol. 193, pp. 281-288 (1948)Hoffman, O., The brittle strength of orthotropic materials, J. Comp. Mat., Vol. 1, pp. 200-206(1967)Koiter, W.T., Stress-strain relations, uniqueness and variational problems for elastic-plastic materialswith a singular yield surface, Q. Appl. Math., Vol. 11, pp. 350-354 (1953)Louren•o, P.B., Analysis of masonry structures with interface elements: Theory and applications,Delft University of Technology, Report 03-21-22-0-01, Delft, The Netherlands (1994)Louren•o, P.B., The elastoplastic homogenisation of masonry structures: With an extension tomasonry structures, Delft University of Technology, Report 03-21-1-31-02, Delft, The Netherlands(1995)Louren•o, P.B., Rots, J.G. and Feenstra, P.H., A ÕtensileÕ Rankine type orthotropic model formasonry, Proc. 3 rd Int. Symp. on Computer Methods in Structural Masonry, Lisbon, Portugal(1995)Ortiz, M. and Popov, E.P., Accuracy and stability of integration algorithms for elastoplastic constitutiverelations, Int. J. Numer. Methods Engrg., Vol. 21, pp. 1561-1576 (1985)Page, A.W., The biaxial compressive strength of brick masonry, Proc. Intsn. Civ. Engrs., Part 2,Vol. 71, pp. 893-906 (1981)
Page 1 and 2: Delft University of TechnologyFacul
Page 3 and 4: TNO-95-NM-R0712 1995 11. INTRODUCTI
Page 5 and 6: TNO-95-NM-R0712 1995 3surfaces sugg
Page 7 and 8: TNO-95-NM-R0712 1995 52. TENSION -
Page 9 and 10: TNO-95-NM-R0712 1995 7τxyτ uσxft
Page 11 and 12: TNO-95-NM-R0712 1995 9whereúκ t =
Page 13 and 14: TNO-95-NM-R0712 1995 11σ n+1 = η
Page 15 and 16: TNO-95-NM-R0712 1995 132.3 Features
Page 17 and 18: TNO-95-NM-R0712 1995 15Ñ The norma
Page 19 and 20: TNO-95-NM-R0712 1995 173. COMPRESSI
Page 21 and 22: TNO-95-NM-R0712 1995 19σ cσ pσ m
Page 23 and 24: TNO-95-NM-R0712 1995 21[MPa]-10.0-8
Page 25 and 26: TNO-95-NM-R0712 1995 238.0/ f myf m
Page 27 and 28: TNO-95-NM-R0712 1995 254. A COMPOSI
Page 29 and 30: TNO-95-NM-R0712 1995 275. EXAMPLESI
Page 31 and 32: TNO-95-NM-R0712 1995 29Horizontal f
Page 33 and 34: TNO-95-NM-R0712 1995 31a) Total def
Page 35 and 36: TNO-95-NM-R0712 1995 33The explanat
Page 37 and 38: TNO-95-NM-R0712 1995 355.2 ETH Zuri
Page 39 and 40: TNO-95-NM-R0712 1995 37For the nume
Page 41 and 42: TNO-95-NM-R0712 1995 39a) Total def
Page 43 and 44: TNO-95-NM-R0712 1995 415.2.2 Wall W
Page 45 and 46: TNO-95-NM-R0712 1995 43c) Cracks d)
Page 47: TNO-95-NM-R0712 1995 455.2.3 Compar
Page 51 and 52: TNO-95-NM-R0712 1995 49APPENDIX APE
Page 53 and 54: TNO-95-NM-R0712 1995 51Plastic step
Page 55: TNO-95-NM-R0712 1995 53-10.0-8.0yxd

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