Localisation analysis in masonry using transformation field analysis

Homogenisation; Localisation; Masonry; Material bifurcation; Transformation field analysis; Localisation analysis; Multi scale analysis; Representative volume element (RVE); Finite element analysis

Abstract :

[en] Transformation field analysis is used for the multi-scale analysis of cracking localisation in masonry. The evaluation of the corresponding consistent homogenised tangent stiffness required in acoustic tensor-based localisation analysis is derived. The average representative volume element mechanical response is studied for two sets of micro-mechanical material laws for mortar joints, based on damage and damage coupled with plasticity. Localisation analyses for stress proportional loading show that meaningful average localisation orientations are properly detected by the acoustic tensor-based loss of ellipticity criterion. The ability of the procedure to reproduce the failure envelope of running bond masonry subjected to uniform biaxial loads is demonstrated. The energetic aspects for the selection of localised solutions are discussed. It is shown that transformation field analysis yields meaningful homogenised localisation results, thereby allowing envisioning its use in nested multi-scale computations. © 2013 Elsevier Ltd.

Disciplines :

Materials science & engineering
Mechanical engineering

Author, co-author :

Chettah, A.; Building, Architecture and Town Planing Department, Université Libre de Bruxelles (ULB), CP 194/2, Av. F.-D. Roosevelt 50, 1050 Brussels, Belgium

Mercatoris, Benoît ; Université Libre de Bruxelles - ULB > Building, Architecture and Town Planning Dept.

Sacco, E.; Department of Civil and Mechanical Engineering, University of Cassino and of the Southern Lazio, Via G. Di Biasio 43, 03043 Cassino, Italy

Massart, T. J.; Building, Architecture and Town Planing Department, Université Libre de Bruxelles (ULB), CP 194/2, Av. F.-D. Roosevelt 50, 1050 Brussels, Belgium

Language :

English

Title :

Localisation analysis in masonry using transformation field analysis

Publication date :

2013

Journal title :

Engineering Fracture Mechanics

ISSN :

0013-7944

eISSN :

1873-7315

Publisher :

Elsevier

Volume :

110

Pages :

166-188

Peer reviewed :

Peer Reviewed verified by ORBi

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Available on ORBi :

since 08 January 2014

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Bibliography

Lourenço PB. Computational strategies for masonry structures. PhD thesis, Delft University of Technology; 1996.
Lourenço P.B. Computations on historic masonry structures. Prog Struct Engng Mater 2002, 4:301-319.
Milani G., Lourenço P.B., Tralli A. Homogenised limit analysis of masonry walls, Part I: Failure surfaces. Comput Struct 2006, 84(3-4):166-180.
Lourenço P.B., de Borst R., Rots J.G. A plane stress softening plasticity model for orthotropic materials. Int J Numer Methods Engng 1997, 40(21):4033-4057.
Berto L., Saetta A., Scotta R., Vitaliani R. An orthotropic damage model for masonry structures. Int J Numer Methods Engng 2002, 55:127-157.
Cecchi A., Di Marco R. Homogenized strategy towards constitutive identification of masonry. J Engng Mech 2002, 128(6):688-697.
Cecchi A., Sab K. A multi-parameter homogenization study for modeling elastic masonry. Eur J Mech A/Solids 2001, 21:249-268.
Anthoine A. Derivation of the in-plane elastic characteristics of masonry through homogenization theory. Int J Solids Struct 1995, 32(2):137-163.
Pegon P., Anthoine A. Numerical strategies for solving continuum damage problems with softening: application to the homogenization of masonry. Comput Struct 1997, 64(1-4):623-642.
Massart T.J., Peerlings R.H.J., Geers M.G.D., Gottcheiner S. Mesoscopic modeling of failure in brick masonry accounting for three-dimensional effects. Engng Fract Mech 2005, 72(8):1238-1253.
Mercatoris B.C.N., Bouillard P., Massart T.J. Multi-scale detection of failure in planar masonry thin shells using computational homogenisation. Engng Fract Mech 2009, 76(4):479-499.
Zucchini A., Lourenço P.B. A micro-mechanical model for the homogenization of masonry. Int J Solids Struct 2002, 39:3233-3255.
Luciano R., Sacco E. Homogenization technique and damage model for old masonry material. Int J Solids Struct 1997, 34(24):3191-3208.
Luciano R., Sacco E. A damage model for masonry structures. Eur J Mech A/Solids 1998, 17(2):285-303.
Massart T.J., Peerlings R.H.J., Geers M.G.D. An enhanced multi-scale approach for masonry wall computations with localization of damage. Int J Numer Methods Engng 2007, 69(5):1022-1059.
Massart T.J., Peerlings R.H.J., Geers M.G.D. Structural damage analysis of masonry walls using computational homogenization. Int J Damage Mech 2007, 16:199-226.
Nguyen V.P., Stroeven M., Sluys L.J. An enhanced continuous-discontinuous multiscale method for modeling mode-I cohesive failure in random heterogeneous quasi-brittle materials. Engng Fract Mech 2012, 79:78-102.
Mercatoris B.C.N., Massart T.J. A coupled two-scale computational scheme for the failure of periodic quasi-brittle thin planar shells and its application to masonry. Int J Numer Methods Engng 2011, 85:1177-1206.
de Bellis M.L., Addessi D. A cosserat based multi-scale model for masonry structures. Int J Multiscale Comput Engng 2011, 9(5):543-563.
Coenen E.W.C., Kouznetsova V.G., Geers M.G.D., Novel boundary conditions for strain localisation analyses in microstructural volume elements Int J Numer Methods Engng 2012, 90(1):1-21.
Dvorak G.J. Transformation field analysis of inelastic composite materials. Proc Roy Soc A 1990, 437:311-327.
Dvorak G.J., Bahei-El-Din Y.A., Wafa A.M. Implementation of the transformation field analysis for inelastic composite materials. Comput Mech 1994, 14:201-228.
Fish J., Shek K., Pandheeradi M., Shephard M.S. Computational plasticity for composite structures based on mathematical homogenization: theory and practice. Comput Methods Appl Mech Engng 1997, 148(1-2):53-73.
Fish J., Yu Q., Shek K. Computational damage mechanics for composite materials based on mathematical homogenization. Int J Numer Methods Engng 1999, 45(11):1657-1679.
Fish J., Shek K. Finite deformation plasticity for composite structures: computational models and adaptive strategies. Comput Methods Appl Mech Engng 1999, 172(1-4):145-174.
Sacco E. A nonlinear homogenization procedure for periodic masonry. Eur J Mech A/Solids 2009, 28:209-222.
Addessi D., Sacco E., Paolone A. Cosserat model for periodic masonry deduced by nonlinear homogenization. Eur J Mech A/Solids 2010, 29:724-737.
Marfia S., Sacco E. Multiscale damage contact-friction model for periodic masonry walls. Comput Methods Appl Mech Engng 2012, 205-208:89-203.
Rice J.R. The localization of plastic deformations. Theoretical and applied mechanics 1976, North-Holland Publishing Company. W.T. Koiter (Ed.).
Rice J.R., Rudnicki J.W. A note on some features of the theory of localization of deformation. Int J Solids Struct 1980, 16:597-605.
Wells G.N., Sluys L.J. A new method for modelling cohesive cracks using finite elements. Int J Numer Methods Engng 2001, 50(12):2667-2682.
Borre G., Maier G. On linear versus nonlinear flow rules in strain localisation analysis. Meccanica 1989, 24:36-41.
Runesson K., Ottosen N.S., Peric D. Discontinuous bifurcations of elastic-plastic solutions at plane stress and plane strain. Int J Plast 1991, 7:99-121.
Ottosen N.S., Runesson K. Properties of discontinuous bifurcation solutions in elasto-plasticity. Int J Solids Struct 1991, 27(4):401-421.
Dragon A., Cormery F., Desoyer T., Halm D. Localised failure analysis using damage models. Localisation and bifurcation theory for soils and rocks 1994, Balkema, Rotterdam. D. Chambon, Vardoulakis (Eds.).
Alfano G., Sacco E. Combining interface damage and friction in a cohesive-zone model. Int J Numer Methods Engng 2006, 68:542-582.
Alfano G., Crisfield MA. Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. Int J Numer Methods Engng 2001, 50:701-1736.
Feyel F., Chaboche J.L. FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fiber SiC/Ti composite materials. Comput Methods Appl Mech Engng 2000, 183(3-4):309-330.
Kouznetsova V.G., Brekelmans W.A.M., Baaijens F.P.T. An approach to micro-macro modeling of heterogeneous materials. Comput Mech 2001, 27(1):37-48.
Simo J.C., Hughes T.J.R. Computational inelasticity 1998, Springer-Verlage, New York.
Chaboche J.L., Kurch S., Maire J.F., Pottier T. Towards a micromechanics based inelastic and damage evolution of composites. Int J Plast 2001, 17:411-439.
Dhanasekar M., Page A.W., Kleeman P.W. The failure of brick masonry under biaxial stresses. Proc Inst Civil Eng 1985, 2:295-313.
Page A.W. The strength of brick masonry under biaxial tension-compression. Int J Masonry Construct 1983, 3:26-31.
van der Pluijm R. Out-of-plane bending of masonry - behaviour and strength. PhD thesis, Eindhoven University of Technology; 1999.
Nguyen V.P., Lloberas-Valls O., Stroeven M., Sluys L.J. Computational homogenization for multiscale crack modeling. Implementational and computational aspects. Int J Numer Methods Engng 2012, 89:192-226.
Mercatoris B.C.N., Massart T.J. Energy consistency in homogenisation-based upscaling scheme for localisation in masonry shells. Int J Fract 2012, 178:259-279.
Michel J.C., Suquet P. Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis. Comput Methods Appl Mech Engng 2004, 139:5477-5502.
Sepe V., Marfia S., Sacco E. A nonuniform TFA homogenization technique based on piecewise interpolation functions of the inelastic field. Int J Solids Struct 2013, 50:725-742.