Acknowledgement
Supported by : CAPES Foundation
References
- Brancherie, D. and Ibrahimbegovic, A. (2009), "Novel anisotrtopic continuum-discrete damage model capable of representing localized failure of massive structures. Part I: theoretical formulation and numerical implementation", Eng. Comput., 26(1-2), 100-127. https://doi.org/10.1108/02644400910924825
- Carol, I., Lopez, C.M. and Roa, O. (2001), "Micromechanical analysis of quasi-brittle materials using fracture-based interface elements", Int. J. Numer. Meth. Eng., 52(1-2), 193-215. https://doi.org/10.1002/nme.277
- Cirak, F., Ortiz, M. and Pandolfi, A. (2005), "A cohesive approach to thin-shell fracture and fragmentation", Comput. Method. Appl. M., 194(21-24), 2604-2618. https://doi.org/10.1016/j.cma.2004.07.048
- Gal, E. and Kryvoruk, R. (2011), "Fiber reinforced concrete properties - a multiscale approach", Comput. Concr., 8 (5), 525-539. https://doi.org/10.12989/cac.2011.8.5.525
- Giusti, S.M., Blanco, P.J., de Souza Neto, E.A. and Feijoo, R.A. (2009), "An assessment of the Gurson yield criterion by a computational multi-scale approach", Eng. Computation, 26(3), 281-301. https://doi.org/10.1108/02644400910943626
- He, H., Stroeven, P., Stroeven, M. and Sluys, L.J. (2011), "Influence of particle packing on fracture properties of concrete", Comput. Concr., 8 (6), 677-692. https://doi.org/10.12989/cac.2011.8.6.677
- Ju, S. H., Stone, J.J. and Rowlands, R.E. (1995), "A new symmetric contact lement stiffness matrix for frictional contact problems", Comput. Struct., 54 (2), 289-301. https://doi.org/10.1016/0045-7949(94)E0176-3
- Michel, J.C., Moulinec, H. and Suquet, P. (1999), "Effective properties of composite materials with periodic microstructure: a computational approach", Comput. Method. Appl. M., 172(1-4), 109-143 https://doi.org/10.1016/S0045-7825(98)00227-8
- Miehe, C., Schroder, J. and Schotte, J., (1999), "Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials", Comput. Method. Appl. M., 171(3-4), 387-418. https://doi.org/10.1016/S0045-7825(98)00218-7
- Nguyen, V.P., Lloberas Valls, O., Stroeven, M. and Sluys, L.J. (2010), "On the existence of representative volumes for softening quasi-brittle materials - a failure zone averaging scheme", Comput. Method. Appl. M., 199 (45-48), 3026-3036.
- Nguyen, V.P., Lloberas Valls, O., Stroeven, M. and Sluys, L.J. (2011), "Homogenization-based multiscale crack modelling: from micro-diffusive damage to macro-cracks", Comput. Method. Appl. M., 200 (9-12), 1220-1236. https://doi.org/10.1016/j.cma.2010.10.013
- Ortiz, M. and Pandolfi, A. (1999), "Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis", Int. J. Numer. Meth. Eng., 44(9), 1267-1282. https://doi.org/10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7
- Paulino, G.H., Celes, W., Espinha, R. and Zhang, Z. (2008), "A general topology-based framework for adaptative isertion of cohesive elements in finite element meshes", Eng. Computation, 24(1), 59-78. https://doi.org/10.1007/s00366-007-0069-7
- Peric, D., de Souza Neto, E.A., Feijoo, R.A., Partovi, M. and Carneiro Molina, A.J. (2011), "On micro-to-macro transitions for multiscale analysis of heterogeneous materials: unified variational basis and finite element Implementation", Int. J. Numer. Meth. Eng., 87(1-5), 149-170. https://doi.org/10.1002/nme.3014
- Pituba, J.J.C. and Fernandes, G.R. (2011), "An anisotropic damage model for concrete", J. Eng. Mech-ASCE., 137(9), 610-624. DOI: 10.1061/(ASCE)EM.1943-7889.0000260.
- Somer, D.D., de Souza Neto, E.A., Dettmer, W.G. and Peric, D. (2009),. "A sub-stepping scheme for multi-scale analysis of solids", Comput. Method. Appl. M., 198(9-12), 1006-1016. https://doi.org/10.1016/j.cma.2008.11.013
- Terada, K., Saiki, I., Matsui. K. and Yamakawa, Y. (2003), "Two-scale kinematics and linearization for simultaneous two-scale analysis of periodic heterogeneous solids at finite strains", Comput. Method. Appl. M., 192(31-32), 3531- 3563. https://doi.org/10.1016/S0045-7825(03)00365-7
- Unger, J.F. and Eckardt, S. (2011a), "Multiscale modeling of concrete", Arch. Comput. Method. E., 18(3), 341-393. https://doi.org/10.1007/s11831-011-9063-8
- Unger, J.F., Eckardt, S. and Konke, C. (2011b), "A mesoscale model for concrete to simulate mechanical failure", Comput. Concr., 8(4), 401-423. https://doi.org/10.12989/cac.2011.8.4.401
- Verhoosel, C.V., Remmers, J.J.C., Gutierrez, M.A. and de Borst, R. (2010), "Computational homogenisation for adhesive and cohesive failure in quasi-brittle solids", Int. J. Numer. Meth. Eng., 83 (8-9), 1155-1179. https://doi.org/10.1002/nme.2854
- Wriggers, P. and Reinelt, J. (2009), "Multi-scale approach for frictional contact of elastomers on rough rigid surfaces", Comput. Method. Appl. M., 198(21-26), 1996-2008. https://doi.org/10.1016/j.cma.2008.12.021
- Wriggers, P. (2006), Computational contact mechanics, Springer-Verlag, Berlin.
- Xiaoyu, J., Jianping, Q., Chenghua, W. and Yu, Z. (2006), "Computer simulation of landslides by the contact element method", Comput. Geosci-UK, 32(4), 434-441. https://doi.org/10.1016/j.cageo.2005.07.004
- Zhu, Q., Kondo, D., Shao, J. and Pensee, V. (2008), "Micromechanical modelling of anisotropic damage in brittle rocks and application", Int. J. Rock Mech. Min., 45(4), 467-477. https://doi.org/10.1016/j.ijrmms.2007.07.014
- Zhu, Q., Kondo, D. and Shao, J. (2009), "Homogenization-based analysis of anisotropic damage in brittle materials with unilateral effect and interactions between microcracks", Int. J. Numer. Anal. Met., 33(6), 749-772. https://doi.org/10.1002/nag.741
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