Abstract
The formulation of constitutive models for anisotropic materials such as masonry is a problem of large complexity. One possible way is to define linear transformations on the stress tensors using fourth-order transformation tensors that carry all the anisotropic information of the material. In the present paper, a new type of evolutionary linear transformation tensor is defined, which can change the values of its components along with the evolution of internal variables. This means the transformation laws are defined according to the current plastic and damage levels, and allows the constitutive model to describe totally different hardening and softening behaviours of the material along different directions. First, a general procedure of formulation of anisotropic constitutive models is given. Second, as a specific example, an orthotropic plastic–damage constitutive model for masonry is presented. Finally, the proposed constitutive model is validated by comparing finite element results with experimental ones pertaining to simple masonry structures under static and cyclic loading.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Tomazevic, M.: Earthquake-Resistant Design of Masonry Buildings. Imperial College Press, London (1999)
Roca, P., Cervera, M., Gariup, G., Pela, L.: Structural analysis of masonry historical constructions. Classical and advanced approaches. Arch. Comput. Methods Eng. 17(3), 299–325 (2010)
Theodossopoulos, D., Sinha, B.: A review of analytical methods in the current design processes and assessment of performance of masonry structures. Constr. Build. Mater. 41, 990–1001 (2013)
Lourenço, P.B.: Computational strategies for masonry structures. Ph.D. thesis, Department of Civil Engineering, Delft University of Technology, Delft, The Netherlands (1996)
Lotfi, H.R., Shing, P.B.: Interface model applied to fracture of masonry structures. J. Struct. Eng. ASCE 120(1), 63–80 (1994)
Tzamtzis, A.: Dynamic finite element analysis of complex discontinuous and jointed structural systems using interface elements. Ph.D. thesis, Department of Civil Engineering, Queen Mary University of London, UK (1994)
Gambarotta, L., Lagomarsino, S.: Damage models for the seismic response of brick masonry shear walls. Part I: the mortar joint model and its applications. Earthq. Eng. Struct. Dyn. 26(4), 423–439 (1997)
Gambarotta, L., Lagomarsino, S.: Damage models for the seismic response of brick masonry shear walls. Part II: the continuum model and its applications. Earthq. Eng. Struct. Dyn. 26(4), 441–462 (1997)
Lourenço, P.B., Rots, J.G.: Multisurface interface model for analysis of masonry structures. J. Eng. Mech. ASCE 123(7), 660–668 (1997)
Sutcliffe, D., Yu, H., Page, A.: Lower bound limit analysis of unreinforced masonry shear walls. Comput. Struct. 79(14), 1295–1312 (2001)
Cervera, M., Oliver, J., Manzoli, O.: A rate-dependent isotropic damage model for the seismic analysis of concrete dams. Earthq. Eng. Struct. Dyn. 25(9), 987–1010 (1996)
Faria, R., Oliver, J., Cervera, M.: A strain-based plastic viscous-damage model for massive concrete structures. Int. J. Solids Struct. 35(14), 1533–1558 (1998)
Hatzigeorgiou, G.D., Beskos, D.E.: Static analysis of 3-D damaged solids and structures by BEM. Eng. Anal. Bound. Elem. 26(6), 521–526 (2002)
Hatzigeorgiou, G.D., Beskos, D.E.: Dynamic inelastic structural analysis by the BEM: a review. Eng. Anal. Bound. Elem. 35(2), 159–169 (2011)
Voyiadjis, G.Z., Kattan, P.I.: Mechanics of damage processes in series and in parallel: a conceptual framework. Acta Mech. 223, 1863–1878 (2012)
Baratta, A., Corbi, H., Corbi, O.: Theorems for masonry solids with brittle time-decaying tensile limit strength. Acta Mech. 228, 837–849 (2017)
Lourenço, P.B., De Borst, R., Rots, J.G.: A plane stress softening plasticity model for orthotropic materials. Int. J. Numer. Methods Eng. 40(21), 4033–4057 (1997)
Lourenço, P.B., Rots, J.G., Blaauwendraad, J.: Continuum model for masonry: parameter estimation and validation. J. Struct. Eng. ASCE 124(6), 642–652 (1998)
Berto, L., Saetta, A., Scotta, R., Vitaliani, R.: An orthotropic damage model for masonry structures. Int. J. Numer. Methods Eng. 55(2), 127–157 (2002)
Bensoussan, A., Lions, J.L., Papanicolau, G.: Asymptotic Analysis for Periodic Structures. North Holland, Amsterdam (1978)
Bakhvalov, N., Panasenko, G.: Homogenization: Averaging Processes in Periodic Media: Mathematical Problems in the Mechanics of Composite Materials. Kluwer Academic, Dordrecht (1989)
Lopez, J., Oller, S., Oñate, E., Lubliner, J.: A homogeneous constitutive model for masonry. Int. J. Numer. Methods Eng. 46(10), 1651–1671 (1999)
Van der Pluijm, R.: Out-of-plane bending of masonry: behaviour and strength. Ph.D. thesis, Department of Architecture, Building and Planning, Eindhoven University of Technology, Eindhoven, The Netherlands (1999)
Zucchini, A., Lourenço, P.: A micro-mechanical model for the homogenisation of masonry. Int. J. Solids Struct. 39(12), 3233–3255 (2002)
Ziegler, F.: Mechanics of Solids and Fluids, 2nd edn. Springer, New York (1995)
Sobotka, Z.: Theorie des plastischen Fließens von anisotropen Kőrpern. Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM) 49(1–2), 25–32 (1969)
Boehler, J., Sawczuk, A.: Equilibre limite des sols anisotropes. J. Mécanique 9(1), 5–33 (1970)
Betten, J.: Applications of tensor functions to the formulation of yield criteria for anisotropic materials. Int. J. Plast. 4(1), 29–46 (1988)
Barlat, F., Lege, D.J., Brem, J.C.: A six-component yield function for anisotropic materials. Int. J. Plast. 7(7), 693–712 (1991)
Karafillis, A., Boyce, M.: A general anisotropic yield criterion using bounds and a transformation weighting tensor. J. Mech. Phys. Solids 41(12), 1859–1886 (1993)
Oller, S., Botello, S., Miquel, J., Oñate, E.: An anisotropic elastoplastic model based on an isotropic formulation. Eng. Comput. 12(3), 245–262 (1995)
Oller, S., Car, E., Lubliner, J.: Definition of a general implicit orthotropic yield criterion. Comput. Methods Appl. Mech. Eng. 192(7), 895–912 (2003)
Pelà, L., Cervera, M., Roca, P.: Continuum damage model for orthotropic materials: application to masonry. Comput. Methods Appl. Mech. Eng. 200(9), 917–930 (2011)
Pelà, L., Cervera, M., Roca, P.: An orthotropic damage model for the analysis of masonry structures. Constr. Build. Mater. 41, 957–967 (2013)
Barlat, F., Aretz, H., Yoon, J., Karabin, M., Brem, J., Dick, R.: Linear transformation-based anisotropic yield functions. Int. J. Plast. 21(5), 1009–1039 (2005)
Barlat, F., Lian, K.: Plastic behavior and stretchability of sheet metals. Part I: a yield function for orthotropic sheets under plane stress conditions. Int. J. Plast. 5(1), 51–66 (1989)
Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Springer, New York (1998)
Lemaitre, J., Chaboche, J.: Mechanics of Solid Materials. Cambridge University Press, Cambridge (1994)
Simo, J., Ju, J.: Strain-and stress-based continuum damage models—I. Formulation. Int. J. Solids Struct. 23(7), 821–840 (1987)
Faria, R., Oliver, J., Cervera, M.: Modeling material failure in concrete structures under cyclic actions. J. Struct. Eng. ASCE 130(12), 1997–2005 (2004)
Lee, J., Fenves, G.L.: Plastic-damage model for cyclic loading of concrete structures. J. Eng. Mech. ASCE 124(8), 892–900 (1998)
Drucker, D.C., Prager, W.: Soil mechanics and plastic analysis or limit design. Q. Appl. Math. 10(2), 157–165 (1952)
Mazars, J.: A description of micro- and macroscale damage of concrete structures. Eng. Fract. Mech. 25(5), 729–737 (1986)
Mazars, J., Pijaudier-Cabot, G.: Continuum damage theory application to concrete. J. Eng. Mech. ASCE 115(2), 345–365 (1989)
Oliver, J., Cervera, M., Oller, S., Lubliner, J.: Isotropic damage models and smeared crack analysis of concrete. In: Proceedings of SCI-C Computer Aided Analysis and Design of Concrete Structures, pp. 987–1010. Pineridge Press, Swansea (1990)
ANSYS Engineering Simulation Software: User’s Manual, Version 13. ANSYS Inc., Canonburg (2010)
Nazar, M.E., Sinha, S.N.: Loading–unloading curves of interlocking grouted stabilised sand–flyash brick masonry. Mater. Struct. 40(7), 667–678 (2007)
Nazar, M.E., Sinha, S.N.: Behavior of interlocking grouted stabilized sand–fly ash brick masonry under uniaxial cyclic compressive loading. J. Mater. Civ. Eng. 19(11), 947–956 (2007)
Raijmakers, T.M.J., Vermeltfoort, A.T.: Deformation controlled meso shear tests on masonry piers. In: Report B-92-1156, TNO-BOUW, Building and Construction Research, Eindhoven University of Technology, The Netherlands (1992)
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper is dedicated to the memory of Franz Ziegler
Rights and permissions
About this article
Cite this article
Fu, Q., Qian, J. & Beskos, D.E. Inelastic anisotropic constitutive models based on evolutionary linear transformations on stress tensors with application to masonry. Acta Mech 229, 719–743 (2018). https://doi.org/10.1007/s00707-017-1995-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-017-1995-0