A 3D multiscale cohesive zone model for quasibrittle materials accounting for friction, damage and interlocking
Keywords:
three-dimensional cohesivezone model, interlocking, mixed-mode fracture, damage-friction couplingAbstract
A three-dimensional (3D) two-scale Cohesive Zone Model (CZM), which is based on a multiplane approach and couples damage with friction and interlocking, is presented for analysing crack propagation in quasi-brittle materials along structural interfaces where formation of cracks is expected. The main idea of the 3D multiplane formulation herein exploited is to describe the asperities of the interface in the form of periodic patterns of inclined planes, denominated Representative Interface Elements (RIE). The interaction within each plane of the RIE is governed by the interface formulation proposed by Alfano and Sacco in earlier work. After reporting details of the formulation and of its algorithmic implementation, the sensitivity of the macroscopic mechanical response to the specific selection of the RIE is analysed and reported with a general numerical assessment of the 3D interface mechanical response to monotonic and cyclic loading histories. A fundamental issue addressed in this paper is the identification of optimal RIE patterns with a minimum number of planes capable of providing isotropic inplane behaviour in response to confined slip tests.
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Alfano, G., & Sacco, E. (2006). Combining interface damage and friction in a cohesive-zone
model. International Journal for Numerical Methods in Engineering, 68, 542–582.
Allegri, G., Jones, M., Wisnom, M., & Hallett, S. (2011). A new semi-empirical model for stress
ratio effect on mode II fatigue delamination growth. Composites Part A: Applied Science and
Manufacturing, 42, 733–740.Barton, N., & Choubey, V. (1977). The shear strength of rock joints in theory and practice.
Rock Mechanics, 10(1–2), 1–54.
Bolzon, G., & Cocchetti, G. (2003). Direct assessment of structural resistance against pressurized
fracture. International Journal for Numerical and Analytical Methods in Geomechanics, 27,
–378.
Brown, S.R., & Scholz, C.H. (1985). Broad bandwidth study of the topography of natural rock
surfaces. Journal of Geophysical Research: Solid Earth (1978–2012), 90, 12575–12582.
Červenka, J., Kishen, J. M. C., & Saouma, V. E. (1998). Mixed mode fracture of cementitious
bimaterial interfaces; part II: Numerical simulation. Engineering Fracture Mechanics, 60,
–107.
Charalambous, G., Allegri, G., Lander, J., & Hallett, S. (2015). A cut-ply specimen for the
mixed-mode fracture toughness and fatigue characterisation of FRPs. Composites Part A:
Applied Science and Manufacturing, 74, 77–87.
Cocchetti, G., Maier, G., & Shen, X. P. (2001). Piecewise linear models for interfaces and mixed
mode cohesive cracks. Computer Modeling in Engineering and Sciences, 3, 279–298.
Cuvilliez, S., Feyel, F., Lorentz, E., & Michel-Ponnelle, S. (2012). A finite element approach
coupling a continuous gradient damage model and a cohesive zone model within the
framework of quasi-brittle failure. Computer Methods in Applied Mechanics and Engineering,
, 244–259.
Del Piero, G., & Raous, M. (2010). A unified model for adhesive interfaces with damage,
viscosity, and friction. European Journal of Mechanics -- A/Solids, 29, 496–507.
Evangelista, F., Roesler, J. R., & Proença, S. P. (2013). Three-dimensional cohesive zone model
for fracture of cementitious materials based on the thermodynamics of irreversible processes.
Engineering Fracture Mechanics, 97, 261–280.
Fouchal, F., Lebon, F., Raffa, M. L., & Vairo, G. (2014). An interface model including cracks
and roughness applied to masonry. Open Civil Engineering Journal, 8, 263–271.
Fouchal, F., Lebon, F., & Titeux, I. (2009). Contribution to the modelling of interfaces in
masonry construction. Construction and Building Materials, 23, 2428–2441.
Foulk, J. W., Allen, D. H., & Helms, K. L. E. (2000). Formulation of a three-dimensional cohesive
zone model for application to a finite element algorithm. Computer Methods in Applied
Mechanics and Engineering, 183, 51–66.
Gasser, T. C., & Holzapfel, G. A. (2006). 3D crack propagation in unreinforced concrete: A
two-step algorithm for tracking 3D crack paths. Computer Methods in Applied Mechanics
and Engineering, 195, 5198–5219.
Giambanco, G., Rizzo, S., & Spallino, R. (2001). Numerical analysis of masonry structures via
interface models. Computer Methods in Applied Mechanics and Engineering, 190, 6493–6511.
Ho, S. L., Joshi, S. P., &Tay, A. (2012). Cohesive zone modeling of 3D delamination in encapsulated
silicon devices. In 2012 IEEE 62nd Electronic Components and Technology Conference (ECTC)
(pp. 1493–1498), San Diego, CA.
Konyukhov, A., Vielsack, P., & Schweizerhof, K. (2008). On coupled models of anisotropic
contact surfaces and their experimental validation. Wear, 264, 579–588.
Kuhn, H. W., & Tucker, A. W. (1951). Nonlinear programming. In Proceedings of 2nd Berkeley
symposium on mathematical statistics and probability (pp. 481–492). Berkeley, CA: University
of California Press.
Lee, H. S., Park, Y. J., Cho, T. F., & You, K. (2001). Influence of asperity degradation on the
mechanical behavior of rough rock joints under cyclic shear loading. International Journal
of Rock Mechanics and Mining Sciences, 38, 967–980.
Licht, C., & Michaille, G. (1997). A modelling of elastic adhesive bonded joints. Advances in
Mathematical Sciences and Applications, 7, 711–740.
Licht, C., Michaille, G., & Pagano, S. (2007). A model of elastic adhesive bonded joints through
oscillation-concentration measures. Journal de mathématiques pures et appliquées, 87, 343–365.Luciano, R., & Sacco, E. (1997). Homogenization technique and damage model for old masonry
material. International Journal of Solids and Structures, 34, 3191–3208.
Macorini, L., & Izzuddin, B. A. (2011). A non-linear interface element for 3D mesoscale analysis
of brick-masonry structures. International Journal for Numerical Methods in Engineering,
, 1584–1608.
Mauge, C., & Kachanov, M. (1994). Effective elastic properties of an anisotropic material with
arbitrarily oriented interacting cracks. Journal of the Mechanics and Physics of Solids, 42,
–584.
Mi, Y., Crisfield, M. A., Davies, G. A. O., & Hellweg, H. B. (1998). Progressive delamination
using interface elements. Journal of Composite Materials, 32, 1246–1272.
Musto, M., & Alfano, G. (2015). A fractional rate-dependent cohesive-zone model. International
Journal for Numerical Methods in Engineering, 105, 313–341.
Radovitzky, R., Seagraves, A., Tupek, M., & Noels, L. (2011). A scalable 3D fracture and
fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element
method. Computer Methods in Applied Mechanics and Engineering, 200, 326–344.
Rafsanjani, S. H., Loureno, P. B., & Peixinho, N. (2014). Dynamic interface model for masonry
walls subjected to high strain rate out-of-plane loads. International Journal of Impact
Engineering, 76, 28–37.
Raous, M., Cangémi, L., & Cocu, M. (1999). A consistent model coupling adhesion, friction,
and unilateral contact. Computer Methods in Applied Mechanics and Engineering, 177,
–399.
Rizzoni, R., Dumont, S., Lebon, F., & Sacco, E. (2014). Higher order model for soft and hard
elastic interfaces. International Journal of Solids and Structures, 51, 4137–4148.
Ruiz, G., Pandolfi, A., & Ortiz, M. (2001). Three-dimensional cohesive modeling of dynamic
mixed-mode fracture. International Journal for Numerical Methods in Engineering, 52,
–120.
Serpieri, R., & Alfano, G. (2011). Bond-slip analysis via a thermodynamically consistent
interface model combining interlocking, damage and friction. International Journal for
Numerical Methods in Engineering, 85, 164–186.
Serpieri, R., Alfano, G., & Sacco, E. (2015). A mixed-mode cohesive-zone model accounting
for finite dilation and asperity degradation. International Journal of Solids and Structures,
–68, 102–115.
Serpieri, R., Sacco, E., & Alfano, G. (2015). A thermodynamically consistent derivation of a
frictional-damage cohesive-zone model with different mode I and mode II fracture energies.
European Journal of Mechanics - A/Solids, 49, 13–25.
Serpieri, R., Varricchio, L., Sacco, E., & Alfano, G. (2014). Bond-slip analysis via a cohesivezone
model simulating damage, friction and interlocking. Fracture and Structural Integrity,
, 284–292.
Simo, J. C., & Hughes, T. J. R. (2008). Computational inelasticity. New York, NY : Springer.
Snozzi, L., & Molinari, J. F. (2013). A cohesive element model for mixed mode loading with
frictional contact capability. International Journal for Numerical Methods in Engineering,
, 510–526.
Sørensen, B. F., & Jacobsen, T. K. (2009). Characterizing delamination of fibre composites by
mixed mode cohesive laws. Composites Science and Technology, 69, 445–456.
Van den Bosch, M. J., Schreurs, P. J. G., & Geers, M. G. D. (2008). On the development of a
D cohesive zone element in the presence of large deformations. Computational Mechanics,
, 171–180.
Zmitrowicz, A. (2006). Models of kinematics dependent anisotropic and heterogeneous
friction. International Journal of Solids and Structures, 43, 4407–4451.
