Abstract
In the present work, the Cohesive/Overlapping Crack Model is extended to the study of masonry or plain concrete structures, which are subjected to off-center compression. Multi-cracking and multi-crushing damage phenomena are simulated by means of the Crack Length Control Scheme, in order to obtain a complete load history of the vaulted structure. This Nonlinear Fracture Mechanics model reveals a high capability in predicting the elastic-plastic-softening behaviour of arches and vaults as well as the local mechanical instabilities, such as snap-back and snap-through, occurring during the post-cracking regime.
In the first part of this paper, the Cohesive/Overlapping Crack Model and a description of the adopted multi-crack numerical procedures is provided. In the second part, some parametric analyses on scale effects in masonry arches are reported together with the results obtained for a real case-study. Finally, some future developments and applications of the model are presented.
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References
Accornero, F., Lacidogna, G., Carpinteri, A.: Medieval arch bridges in the Lanzo Valleys, Italy: cases studies on incremental structural analysis and fracturing benefit. J. Bridge Eng. (ASCE) 23(7), 05018005 (2018)
Manuello Bertetto, A., Marano, G.C.: Numerical and dimensionless analytical solutions for circular arch optimization. Eng. Struct. 253, 113360 (2022)
Melchiorre, J., Manuello Bertetto, A., Marmo, F., Adriaenssens, S., Marano, G.C.: Differential formulation and numerical solution for elastic arches with variable curvature and tapered cross-sections. Eur. J. Mech.-A/Solids 97, 104757 (2023)
Carpinteri, A., Lacidogna, G., Accornero, F.: Evolution of the fracturing process in masonry arches. J. Struct. Eng. (ASCE) 141(5), 04014132 (2015)
Accornero, F., Lacidogna, G., Carpinteri, A.: Evolutionary fracture analysis of masonry arches: effect of shallowness ratio and size scale. Comptes Rendus Mécanique 344(9), 623–630 (2016)
Heyman, J.: The Stone Skeleton, 1st edn. Cambridge University Press, Cambridge, UK (1995)
Lacidogna, G., Accornero, F.: Elastic, plastic, fracture analysis of masonry arches: a multi-span bridge case study. Curved Layered Struct. 5, 1–9 (2018)
Accornero, F., Lacidogna, G.: Safety assessment of masonry arch bridges considering the fracturing benefit. Appl. Sci. 10(10), 3490 (2020)
Carpinteri, A., Corrado, M., Mancini, G., Paggi, M.: Size-scale effects on plastic rotational capacity of reinforced concrete beams. Struct. J. (ACI) 106(06), 887–896 (2009)
Carpinteri, A., Corrado, M., Paggi, M., Mancini, G.: New model for the analysis of size-scale effects on the ductility of reinforced concrete elements in bending. J. Eng. Mech. (ASCE) 135(3), 221–229 (2009)
Carpinteri, A., Corrado, M.: Upper and lower bounds for structural design of RC members with ductile response. Eng. Struct. 33(12), 3432–3441 (2011)
Accornero, F., Cafarelli, R., Carpinteri, A.: Cracking and crushing in prestressed concrete beams. Struct. J. (ACI) 118(2), 101–109 (2021)
Accornero, F., Cafarelli, R., Carpinteri, A.: The cohesive/overlapping crack model for plain and RC beams: scale effects on cracking and crushing failures. Mag. Concr. Res. 74(9), 433–450 (2022)
Accornero, F., Cafarelli, R., Carpinteri, A., Nanni, A.: Scale effects in GFRP-bar reinforced concrete beams. Struct. Concr. 24(2), 2817–2826 (2023)
Carpinteri, A., Accornero, F., Cafarelli, R.: Scale effects in prestressed concrete structures: maximum reinforcement percentage to avoid brittle crushing. Eng. Struct. 225, 113911 (2022)
Hillerborg, A., Modéer, M., Petersson, P.-E.: Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Concr. Res. 6(6), 773–781 (1976)
Carpinteri, A.: Cusp catastrophe interpretation of fracture instability. J. Mech. Phys. Solids 37(5), 567–582 (1989)
Belgin, C.M., Șener, S.: Size effect on failure of overreinforced concrete beams. Eng. Fract. Mech. 75(8), 2308–2319 (2008)
Lourenco, P.B.: Computational strategies for masonry structures, PhD Thesis, Delft University of Technology, Netherlands (1996)
Carpinteri, A., Corrado, M., Mancini, G., Paggi, M.: The overlapping crack model for uniaxial and eccentric concrete compression tests. Mag. Concr. Res. 61(9), 745–757 (2009)
Lanczos, C.: The Variational Principles of Mechanics, 4th edn. Dover Publication, New York, USA (1949)
Bocca, P., Carpinteri, A., Valente, S.: Mixed mode fracture of concrete. Int. J. Solids Struct. 27(9), 1139–1153 (1991)
Ramm, E.: Strategies for tracing the nonlinear response near limit points. In: Wunderlich, W., Stein, E., Bathe, K.-J. (eds.) Nonlinear Finite Element Analysis in Structural Mechanics, pp. 63–89. Springer Berlin Heidelberg, Berlin, Heidelberg (1981). https://doi.org/10.1007/978-3-642-81589-8_5
Goodman, R.E., Taylor, R.L., Brekke, T.L.: A model for the mechanics of jointed rock. J. Soil Mech. Found. Div. (ASCE) 94(3), 637–659 (1968)
Nguyen, V.P.: Discontinuos Galerkin/extrinsic cohesive zone modelling: implementation caveats and applications in computational fracture mechanics. Eng. Fract. Mech. 128, 37–68 (2014)
D’Altri, A.M., et al.: Modeling strategies for the computational analysis of unreinforced masonry structures: review and classification. Arch. Comput. Methods Eng. 27, 1153–1185 (2020)
Castigliano, A.: Théorie de l’Equilibre des Systémes Elastiques et ses Applications. 1st edn. Del Negro, Torino, Italy (1879)
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Cafarelli, R., Accornero, F., Carpinteri, A. (2024). Snap-Back Analysis of Fracture Evolution in Multi-cracked Masonry Arches. In: Gabriele, S., Manuello Bertetto, A., Marmo, F., Micheletti, A. (eds) Shell and Spatial Structures. IWSS 2023. Lecture Notes in Civil Engineering, vol 437. Springer, Cham. https://doi.org/10.1007/978-3-031-44328-2_9
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