The continuous-discontinuous Galerkin method applied to crack propagation |
Forti, Tiago L.D.
(Simworx R&D)
Forti, Nadia C.S. (Pontifical Catholic University of Campinas) Santos, Fabio L.G. (Simworx R&D) Carnio, Marco A. (Evolucao Engenharia) |
1 | Asferg, J.L., Poulsen, P.N. and Nielsen, L.O. (2007), "A direct XFEM formulation for modeling of cohesive crack growth in concrete", Comput. Concrete, 4(2), 83-100. DOI |
2 | Barenblatt, G.I. (1959), "The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axiallysymmetric cracks", J. Appl. Math. Mech., 23, 622-636. DOI |
3 | Barenblatt, G.I. (1962), "The mathematical theory of equilibrium of crack in brittle fracture", Adv. Appl. Mech., 7, 55-129. DOI |
4 | Cangiani, A., Chapman, J., Georgoulis, E.H. and Jensen, M. (2013), "On the stability of continuous-discontinuous Galerkin methods for advection-diffusion-reaction problems", J. Scientif. Comput., 57, 313-330. DOI |
5 | Cangiani, A., Chapman, J., Georgoulis, E.H. and Jensen, M. (2014), "On local super-penalization of interior penalty discontinuous Galerkin methods", Int. J. Numer. Anal. Mod., 11(3), 478-495. |
6 | Dawson, C. and Proft, J. (2002), "Coupling of continuous and discontinuous Galerkin methods for transport problems, Comput", Meth. Appl. Mech. Eng., 191, 3213-3231. DOI |
7 | Devloo, P.R.B., Forti, T.L.D. and Gomes, S.M. (2007), "A combined continuous-discontinuous finite element method for convection-diffusion problems", Latin Am. J. Solid. Struct., 4, 229-246. |
8 | Dong, Y., Wu, S., Xu, S.S., Zhang, Y. and Fang, S. (2010), "Analysis of concrete fracture using a novel cohesive crack method", Appl. Math. Model., 34, 4219-4231. DOI |
9 | Elsaigh, W.A. (2001), "Steel fiber reinforced concrete ground slabs: a comparative evaluation of plain and steel fiber reinforced concrete ground slabs", Master Dissertation, University of Pretoria, South Africa. |
10 | Elsaigh, W.A., Kearsley, E.P. and Robberts, J.M. (2011), "Modeling the behavior of steel-fiber reinforced concrete ground slabs. II: Development of slab nodel", J. Transp. Eng., 137, 889-896. DOI |
11 | Feng, D.C. and Wu, J.Y. (2018), "Phase-field regularized cohesive zone model (CZM) and size effect of concrete", Eng. Fract. Mech., 197, 66-79. DOI |
12 | Kh, H. M., O zakca, M., Ekmekyapar, T, and Kh, A. M. (2016), "Flexural behavior of concrete beams reinforced with different types of fibers", Comput. Concrete, 18(5), 999-1018. DOI |
13 | Forti, T.L.D., Farias, A.M., Devloo, P.R.B. and Gomes, S.M. (2016), "A comparative numerical study of different finite element formulations for 2D model elliptic problems: Continuous and discontinuous Galerkin, mixed and hybrid methods", Finite Elem. Anal. Des., 115, 9-20. DOI |
14 | Gamino, A.L., Manzoli, O.L, Sousa, J.L.A.O. and Bittencourt, T.N. (2010), "2D evaluation of crack openings using smeared and embedded crack models", Comput. Concrete, 7(6), 483-496. DOI |
15 | Hillerborg, A., Modeer, M. and Petersson, P. (1976), "Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements", Cement Concrete Res., 6, 773-782. DOI |
16 | Hordijk, A.D. (1991), "Local approach to fatigue of concrete", Doctoral Thesis, Delft University of Technology, The Netherlands. |
17 | Hu, S., Xu, A., Hu, X. and Yin, Y. (2016), "Study on fracture characteristics of reinforced concrete wedge splitting tests", Comput. Concrete, 18(3), 337-354. DOI |
18 | Kurumatani, M., Soma, Y. and Terada, K. (2019), "Simulations of cohesive fracture behavior of reinforced concrete by a fracturemechanics-based damage model", Eng. Fract. Mech., 206, 392-407. DOI |
19 | Larson, M.G. and Niklasson, A.J. (2001), "Conservation properties for the continuous and discontinuous Galerkin methods", Tech. Rep. 2000-08, Chalmers University of Technology. |
20 | Lin, H.X., Lu, J.Y. and Xu, B. (2017), "Numerical approach to fracture behavior of CFRP/concrete bonded interfaces", Comput. Concrete, 20(3), 291-295. DOI |
21 | Suarez, F., Galvez, J.C., Enfedaque, A. and Alberti, M.G. (2019), "Modelling fracture on polyolefin fibre reinforced concrete specimens subjected to mixed-mode loading", Eng. Fract. Mech., 211, 244-253. DOI |
22 | Murthy, A.R., Ganesha, P., Kumarb, S.S. and Iyerc, N.R. (2015), "Fracture energy and tension softening relation for nanomodified concrete", Struct. Eng. Mech., 54(6), 1201-1216. DOI |
23 | Oden, J.T., Babuska, I. and Baumann, C.E. (1998), "A discontinuous hp finite element method for diffusion problems", J. Comput. Phys., 146, 491-519. DOI |
24 | Oden, J.T., Carey, G.F. and Becker, E.B. (1981), Finite Elements: An Introduction, Prentice Hall Inc., New Jersey, USA. |
25 | Rosa, A.L., Yu, R.C., Ruiz, G., Saucedo, L. and Sousa, J.L.A.O. (2012), "A loading rate dependent cohesive model for concrete fracture", Eng. Fract. Mech., 82, 195-208. DOI |
26 | Santos, F.L.G. and Souza, J.L.A.O. (2015), "Determination of parameters of a viscous-cohesive fracture model by inverse analysis", Ibracon Struct. Mater. J., 8, 669-706. DOI |
27 | Suli, E., Schwab, C. and Houston, P. (2000), "hp-DGFEM for Partial Differential Equations with Nonnegative Characteristic Form". Eds. Cockburn, B., Karniadakis, G.E. and Shu, C.W., Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering, 11, 221-230. |
28 | Yaylaci, M. (2016), "The investigation crack problem through numerical analysis", Struct. Eng. Mech., 57(6), 1143-1156. DOI |
29 | Yu, R.C., Zhang, X. and Ruiz, G. (2008), "Cohesive modeling of dynamic fracture in reinforced concrete", Comput. Concrete, 5(4), 389-400. DOI |