Abstract
The paper focuses on the problem of developing a reliable theoretical model for representing the bodies that exhibit a heterogeneous mechanical behaviour in tension and in compression. The proposed phenomenological model is characterized by an evolutionary tensile strength that is ruled by a decay law depending on the loading path. Such model is of particular interest, since it may be successfully employed, after suitable calibration of the tensile strength, for managing a class of materials that includes masonry bodies. In the paper, the fundamental postulates under multi-axial stress states are formulated and proved to hold at any stage of the loading path. The relationships of the solution of the introduced elastic–brittle model with solutions relevant to other more standard and well-behaved mechanical models are analytically investigated. Finally, two original theorems are enounced that allow to identify some upper and lower bounds on the solution, in energy terms.
Similar content being viewed by others
References
Heyman J.: The stone skeleton. J. Solids Struct. 2, 249–279 (1966)
Kooharian A.: Limit analysis of voussoir (segmental) and concrete arches. J. Am. Concrete Inst. 24, 317–328 (1952)
Khludnev, A.M., Kovtunenko V.A.: Analysis of cracks in solids. International series on advances in fracture mechanics 6, p. 408. WIT-Press, Southampton, Boston (2000)
Del Piero G.: Constitutive equation and compatibility of the external loads for linear-elastic masonry materials. Meccanica 24, 150–162 (1989)
Baratta A., Corbi O.: An approach to masonry structural analysis by the no-tension assumption—Part II: Load singularities, numerical implementation and applications. Appl. Mech. Rev. ASME Int. 63, 040803-1/21 ISSN 0003-6900 (2010). doi:10.1115/1.4002791
Baratta A., Corbi O.: On the statics of no-tension masonry-like vaults and shells: solution domains, operative treatment and numerical validation. Ann. Solid Struct. Mech. 2, 107–122 ISSN 1867-6936 (2011). doi:10.1007/s12356-011-0022-8
Andreu, A., Gil, L., Roca, P.: Limit analysis of masonry constructions by 3D funicular modeling. In: Lourenço P.B., et al. (eds.) Structural analysis of historical constructions, pp 1135–1142. MacMillan, New Deli (2006)
Bazant Z.P., Li Y.N.: Stability of cohesive crack model: Part I: Energy principles. J. Appl. Mech. 62, 959–964 (1995)
Corbi O., Candela M.: About the structural restoration of the S. Domenico’s monastery in Naples. Int. J. Mech. 7, 393–400 (2013)
Gilbert, M.: Limit analysis applied to masonry arch bridges: state-of-the-art and recent developments. In: Arch Bridges ‘07, Funchal, Madeira, pp. 13–28 (2007)
Lemos, J. : Assessment of the ultimate load of a masonry arch using discrete elements. In: Middleton, J., Pande, G.N. (eds.) Computer, methods in structural masonry, pp. 294–302. Books & Journals International, Swansea (1995)
Lucchesi M., Padovani C., Pasquinelli G., Zani N.: Statics of masonry vaults, constitutive model and numerical analysis. J. Mech. Mater. Struct. 2, 221–244 (2007)
Pietruszczak S., Ushaksaraei R.: Description of inelastic behaviour of structural masonry. Int. J. Solids Struct. 40, 4003–4019 (2003). doi:10.1016/S0020-7683(03)00174-4
Roca P., Cervera M., Gariup G., Pela L.: Structural analysis of masonry historical constructions. Classical and advanced approaches. Arch. Comput. Methods Eng. 17, 299–325 (2010)
Baratta A., Corbi O.: Contribution of the fill to the static behaviour of arched masonry structures: theoretical formulation. Acta Mech. 225, 53–66 (2014). doi:10.1007/s00707-013-0935-x
Baratta A., Corbi I.: Equilibrium models for helicoidal laterally supported staircases. Int. J. Comput. Struct. 124, 21–28 (2013). doi:10.1016/j.compstruc.2012.11.007
Baratta A., Corbi I.: Statics and equilibrium paths of masonry stairs. Open Constr. Build. Technol. J. 6, 368–372 ISSN: 1874-8368 (2012). doi:10.2174/1874836801206010368
Baratta A., Corbi I.: Topology optimization for reinforcement of no-tension structures. Acta Mech. 225, 663–678 (2014). doi:10.1007/s00707-013-0987-y
Furtmüller T., Adam C.: Numerical modeling of the in-plane behavior of historical brick masonry walls. Acta Mech. 221, 65–77 (2011). doi:10.1007/s00707-011-0493-z
Elmalich D., Rabinovitch O.: Nonlinear analysis of masonry arches strengthened with composite materials. J. Eng. Mech. 136, 996–1005 (2010). doi:10.1061/(ASCE)EM.1943-7889.0000140
D’Ambrisi A., Feo L., Focacci F.: Masonry arches strengthened with composite unbonded tendons. J. Compos. Struct. 98, 323–329 (2013). doi:10.1016/j.compstruct.2012.10.040
Corbi I.: FRP reinforcement of masonry panels by means of C-fiber strips. Compos. B Eng. 47, 348–356 ISSN: 13598368 (2013). doi:10.1016/j.compositesb.2012.11.005t
Baratta, A., Corbi, I., Corbi, O.: Bounds on the elastic brittle solution in bodies reinforced with FRP/FRCM composite provisions. Compos. Part B Eng. 68, 230–236 (2014). doi:10.1016/j.compositesb.2014.07.027
Corbi O., Zaghw A.H., Elattar A., Saleh A.: Preservation provisions for the environmental protection of Egyptian monuments subject to structural vibrations. Int. J. Mech. 7, 172–179 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Baratta, A., Corbi, O. Heterogeneously resistant elastic–brittle solids under multi-axial stress: fundamental postulates and bounding theorems. Acta Mech 226, 2077–2087 (2015). https://doi.org/10.1007/s00707-015-1299-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-015-1299-1