Abstract
Despite its texture as a periodic composite material, masonry is generally modelled as a ‘concrete-like’ material, so that its anisotropic nature is not taken into account. A way to derive an enhanced constitutive model for masonry, closely related to the behaviour of its constituent materials (mortar and bricks) and to its geometry (bond pattern, thickness of the mortar joints, etc.), is to take advantage of the homogenization techniques, which have been extensively developed for composite materials. Among them, the homogenization theory for periodic media seems particularly suitable. According to this theory, the global behaviour of masonry may be derived by solving a boundary value problem on a small domain to be repeated by translation (cell) with particular boundary conditions (periodicity) and special type of loading (average of strain and/or stress). This problem turns out to be generally well posed: in linear elasticity, it yields the macroscopic elastic characteristics of masonry (in the case of running bond masonry, the four constants defining the equivalent orthotropic material) [1]. In the non-linear range (damage or plasticity), it may be used to determine the failure criterion of the homogenized material: in the stress (or strain) space, radial loading paths are imposed and, for each direction considered, the maximum stress, the corresponding strain and the pattern of failure are determined.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anthoine, A., Derivation of the in-plane elastic characteristics of masonry through homogenization theory. Int. J. Solids Struct., 32(2) (1995) 137–163.
Maier, G., Nappi, A. and Papa, E., Damage models for masonry as a composite material: a numerical and experimental analysis. In Constitutive Laws for Engineering Materials (eds Desai, C.S., et al.). ASME Press, New York (1991) pp. 427–432.
Pande, G.N., Liang, J.X. and Middleton, J., Equivalent elastic moduli for brick masonry. Computers and Geotechnics, 8(5) (1989) 243–265.
Love, A.E.H., A Treatise on the Mathematical Theory of Elasticity. Dover Publications, New York, 1944.
Milne-Thomson, L.M., Plane and Antiplane Elastic Systems. Springer-Verlag, Berlin, 1960.
Lekhnitskii, S.G., Theory of Elasticity of an Anisotropic Body. MIR, Moscow, 1981.
Saada, A.S., Elasticity: Theory and Application. Pergamon Press, Oxford, 1974.
Pietruszczak, S. and Niu, X., A mathematical description of macroscopic behaviour of brick masonry. Int. J. Solids Struct., 29(5) (1992) 531–546.
Bensoussan, A., Lions, J.-L. and Papanicolaou, G., Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam, 1978.
Duvaut, G., Homogénéisation et matériaux composites. In Trends and Applications of Pure Mathematics to Mechanics (Lecture Notes in Physics 195) (eds Ciariet, P.G. and Roseau, M.). Springer, Berlin (1984), pp. 35–62.
Sanchez-Palencia, E., Non-homogeneous Media and Vibration Theory (Lecture Notes in Physics 127). Springer, Berlin, 1980.
Dhanasekar, M, Page, A.W. and Kleeman, P.W., The elastic properties of brick masonry. Int. J. Masonry Construct., 2(4) (1982) 155–160.
Suquet, P.-M., Elements of homogenization for inelastic solid mechanics. In Homogenization Techniques for Composite Media (eds Sanchez-Palencia, E. and Zaoui, A.) Springer-Verlag, Berlin, 1987, pp. 193–279.
Page, A.W., Finite element model for masonry. ASCE J. Struct. Engng, 104(8) (1978) 1267–1285.
Lotfi, H.R. and Shing, P.B., Interface model applied to fracture of masonry structures. ASCE J. Struct. Engng, 120(1) (1994) 63–80.
Lourenço, P.B., Rots, J.G. and Blaauwendraad, J., Implementation of an interface cap model for the analysis of masonry structures. In Computational Modelling of Concrete Structures (Vol. 1) (eds Mang, H., et al.). Pineridge Press, Swansea, 1994, pp. 123–134.
Mazars, J., A description of micro- and macroscale damage of concrete structures. Engng Tract. Mech., 25 (1986) 729–737.
Bazant, Z.P., Numerical simulation of progressive fracture in concrete structures: recent developments. In Computer Aided Analysis and Design of Concrete Structures (Part 1) (eds Damjanic, F., et al.). Pineridge Press, Swansea, 1984, pp. 1–18.
Willam, K.J., Experimental and computational aspects of concrete fracture. In Computer Aided Analysis and Design of Concrete Structures (Part 1) (eds Damjanic, F., et al.). Pineridge Press, Swansea, 1984, pp. 33–70.
de Borst, R., Muhlhaus, H.B., Pamin, J., et al., Computational modelling of localization of deformation. In Computational Plasticity (Part 1) (eds Owen, D.R.J., et al.). Pineridge Press, Swansea, 1992, pp. 483–508.
Pijaudier-Cabot, G. and Bazant, Z.P., Non local damage theory. ASCE J. Engng Mech., 113 (1987) 1512–1533.
Mazars, J., Pijaudier-Cabot, G. and Saouridis, C, Size effect and continuous damage in cementitious materials. Int. J. Tract., 51 (1991) 159–173.
Bazant, Z.P. and Pijaudier-Cabot, G., Non local continuum damage, localization instability and convergence. ASME J. Appl. Mech., 55 (1988) 287–293.
CASTEM 2000, Guide d’utilisation. CEA, Saclay, 1990.
Verpeaux, P., Millard, A., Charras, T., et al., A modern approach of large computer codes for structural analysis. In Transactions of the 10th SMIRT Conference (Vol. B) (ed. Hadjian, A.H.), AASMIRT, Los Angeles, 1989, pp. 75–78.
Charras, T., Millard, A. and Verpeaux, P., Solution of 2D and 3D contact problems by mean of Lagrange multipliers in the CASTEM 2000 finite element program. In Proceedings of the Conference on Contact Mechanics (eds Aliabadi, M.H. and Brebbia, C.A.), Computer Mechanics Publication, Southampton, 1993, pp. 183-194.
Swan, C.C., Techniques for stress- and strain-controlled homogenization of inelastic periodic composites. Computer Meth. Appl. Mech. Engng, 111 (1994) 249–267.
Pegon, P. and Anthoine, A., Numerical strategies for solving continuum damage problems involving softening: application to the homogenization of masonry. In Advances in Non-linear Finite Element Methods (eds Topping, B.H.V. and Papadrakakis, M.). Civil- Comp Press, Edinburgh, 1994, pp. 143-157.
Pijaudier-Cabot, G. and Huerta, A., Finite element analysis of bifurcation in non-local strain softening solids. Computer Meth. Appl. Mech. Engng, 90 (1991) 905–919.
Crisfield, M.A., Non-linear Finite Element Analysis of Solids and Structures (Vol. 1). J. Wiley and Sons, Chichester, 1991.
Riks, E., An incremental approach to the solution of snapping and buckling problems. Int. J. Solids Struct., 15 (1979) 529–551.
Wempner, G.A., Discrete approximations related to non linear theories of solids. Int. J. Solids Struct., 7 (1971) 1581–1599.
Anthoine, A., In-plane behaviour of masonry: a literature review (Report EUR 13840 EN). European Commission, Luxembourg, 1991.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Anthoine, A., Pegon, P. (1996). Numerical analysis and modelling of the damage and softening of brick masonry. In: Bull, J.W. (eds) Numerical Analysis and Modelling of Composite Materials. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0603-0_7
Download citation
DOI: https://doi.org/10.1007/978-94-011-0603-0_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4266-6
Online ISBN: 978-94-011-0603-0
eBook Packages: Springer Book Archive