Abstract
This Chapter presents continuous models to describe concrete behaviour in a quasi-static regime during monotonic and cyclic loading. In the case of monotonic loading, isotropic elasto-plastic, isotropic damage and smeared crack model, and in the case of cyclic loading elasto-plastic-damage models are described. An integral-type non-local and a second gradient approaches to model strain localization are introduced. In addition, bond-slip laws are presented.
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References
ABAQUS. Theory Manual, Version 5.8, Hibbit, Karlsson & Sorensen Inc. (1998)
Aifantis, E.C.: Update on class of gradient theories. Mechanics of Materials 35(3), 259–280 (2003)
Akkermann, J.: Rotationsverhalten von Stahlbeton-Rahmenecken. PhD Thesis, Universität Fridericiana zu Karlsruhe, Karlsruhe (2000)
Asferg, P.N., Poulsen, P.N., Nielsen, L.O.: Modelling of crack propagation in concrete applying the XFEM. In: Meschke, G., de Borst, R., Mang, H., Bicanic, N. (eds.) Computational Modelling of Concrete Structures, EURO-C, pp. 33–42. Taylor and Francis (2006)
Askes, H., Sluys, L.J.: A classification of higher-order strain gradient models in damage mechanics. Archive of Applied Mechanics 53(5-6), 448–465 (2003)
Bazant, Z.P., Bhat, P.D.: Endochronic theory of inelasticity and failure of concrete. Journal of Engineering Mechanics Division ASCE 102(4), 701–722 (1976)
Bazant, Z.: Endochronic inelasticity and incremental plasticity. International Journal of Solids and Structures 14(9), 691–714 (1978)
Bazant, Z.P., Shieh, C.L.: Endochronic model for nonlinear triaxial behaviour of concrete. Nuclear Engineering and Design 47(2), 305–315 (1978)
Bazant, Z.P., Cedolin, L.: Blunt crack band propagation in finite element analysis. Journal of Engineering Mechanics Division ASCE 105(2), 297–315 (1979)
Bazant, Z.P., Oh, B.H.: Crack band theory for fracture of concrete. Materials and Structures RILEM 16(93), 155–177 (1983)
Bazant, Z.P., Lin, F.: Non-local yield limit degradation. International Journal for Numerical Methods in Engineering 26(8), 1805–1823 (1988)
Bazant, Z., Ozbolt, J.: Non-local microplane model for fracture, damage and size effect in structures. Journal of Engineering Mechanics ASCE 116(11), 2485–2505 (1990)
Bazant, Z., Jirasek, M.: Nonlocal integral formulations of plasticity and damage: survey of progress. Journal of Engineering Mechanics 128(11), 1119–1149 (2002)
Belytschko, T., Moes, N., Usui, S., Parimi, C.: Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 50(4), 993–1013 (2001)
Belytschko, T., Gracie, R., Ventura, G.: A review of extended/generalized finite element methods for material modeling. Modelling and Simulation in Material Science and Engineering 17(4), 1–24 (2009)
Bhandari, A.R., Inoue, J.: Experimental study of strain rates effects on strain localization characteristics of soft rocks. Soils and Foundations 45(1), 125–140 (2005)
Bobinski, J., Tejchman, J.: Numerical simulations of localization of deformation in quasi-brittle materials within non-local softening plasticity. Computers and Concrete 1(4), 433–455 (2004)
Bobiński, J., Tejchman, J.: Modelling of strain localization in quasi-brittle materials with a coupled elasto-plastic-damage model. International Journal for Theoretical and Applied Mechanics 44(4), 767–782 (2006)
Bobiński, J.: Implementacja i przykłady zastosowań nieliniowych modeli betonu z nielokalnym osłabieniem. PhD Thesis, Gdańsk University of Technology (2006)
Bobiński, J., Tejchman, J.: Continuous and discontinuous modeling of cracks in concrete elements. In: Bicanic, N., de Borst, R., Mang, H., Meschke, G. (eds.) Modelling of Concrete Structures, pp. 263–270. Taylor and Francis Group, London (2010)
Bolander, J.E., Sukumar, N.: Irregular lattice model for quasi-static crack propagation. Physical Review B 71(9), 094106(2005)
Borino, G., Failla, B., Parrinello, F.: A symmetric nonlocal damage theory. International Journal of Solids and Structures 40(13-14), 3621–3645 (2003)
Brinkgreve, R.B.J.: Geomaterial models and numerical analysis of softening. Phd Thesis, Delft University of Technology (1994)
Caballero, A., Carol, I., Lopez, C.M.: New results in 3d meso-mechanical analysis of concrete specimens using interface elements. In: Meschke, G., de Borst, R., Mang, H., Bicanic, N. (eds.) Computational Modelling of Concrete Structures, EURO-C, pp. 43–52. Taylor and Francis (2006)
Caballero, A., Carol, I., Lopez, C.M.: 3D meso-mechanical analysis of concrete specimens under biaxial loading. Fatigue and Fracture of Engineering Materials and Structures 30(9), 877–886 (2007)
Carol, I., López, C.M., Roa, O.: Micromechanical analysis of quasi-brittle materials using fracture-based interface elements. International Journal for Numerical Methods in Engineering 52(1-2), 193–215 (2001)
Carol, I., Willam, K.: Spurious energy dissipation/generation in stiffness recovery models for elastic degradation and damage. International Journal of Solids and Structures 33(20-22), 2939–2957 (1996)
Carol, I., Rizzi, E., Willam, K.: On the formulation of anisotropic elastic degradation. International Journal of Solids and Structures 38(4), 491–518 (2001)
CEB-FIP Model Code 90, London (1992)
Chambon, R., Caillerie, D., Matsuchima, T.: Plastic continuum with microstructure, local second gradient theories for geomaterials: localization studies. International Journal of Solids and Structures 38(46-47), 8503–8527 (2001)
Chen, E.: Non-local effects on dynamic damage accumulation in brittle solids. International Journal for Numerical and Analytical Methods in Geomechanics 23(1), 1–21 (1999)
Chen, J., Yuan, H., Kalkhof, D.: A non-local damage model for elastoplastic materials based on gradient plasticity theory. Report Nr.01-13, Paul Scherrer Institut, 1–130 (2001)
Cope, R.J., Rao, P.V., Clark, L.A., Norris, P.: Modeling of concrete reinforced behavior for finite element analysis of bridge slabs. Numerical Methods for Non-linear Problems 1, 457–470 (1980)
Cusatis, G., Bazant, Z.P., Cedolin, L.: Confinement-shaer lattice model for concrete damage in tension and compression: I. Theory. Journal for Engineering Mechanics ASCE 129(12), 1439–1448 (2003)
de Borst, R., Nauta, P.: Non-orthogonal cracks in a smeared finite element model. Engineering Computations 2(1), 35–46 (1985)
de Borst, R.: Non-linear analysis of frictional materials. Phd Thesis, University of Delft (1986)
de Borst, R., Mühlhaus, H.-B., Pamin, J., Sluys, L.B.: Computational modelling of localization of deformation. In: Owen, D.R.J., Onate, H., Hinton, E. (eds.) Proc. of the 3rd Int. Conf. Comp. Plasticity, Swansea, pp. 483–508. Pineridge Press (1992)
de Borst, R., Mühlhaus, H.-B.: Gradient dependent plasticity: formulation and algorithmic aspects. International Journal for Numerical Methods in Engineering 35(3), 521–539 (1992)
de Borst, R., Pamin, J.: Some novel developments in finite element procedures for gradient-dependent plasticity. International Journal for Numerical Methods in Engineering 39(14), 2477–2505 (1996)
de Vree, J.H.P., Brekelmans, W.A.M., van Gils, M.A.J.: Comparison of nonlocal approaches in continuum damage mechanics. Computers and Structures 55(4), 581–588 (1995)
den Uijl, J.A., Bigaj, A.: A bond model for ribbed bars based on concrete confinement. Heron 41(3), 201–226 (1996)
di Prisco, C., Imposimato, S., Aifantis, E.C.: A visco-plastic constitutive model for granular soils modified according to non-local and gradient approaches. International Journal for Numerical and Analytical Methods in Geomechanic 26(2), 121–138 (2002)
D’Addetta, G.A., Kun, F., Ramm, E.: On the application of a discrete model to the fracture process of cohesive granular materials. Granular Matter 4(2), 77–90 (2002)
Donze, F.V., Magnier, S.A., Daudeville, L., Mariotti, C.: Numerical study of compressive behaviour of concrete at high strain rates. Journal of Engineering Mechanics ASCE 125(10), 1154–1163 (1999)
Dörr, K.: Ein Beitag zur Berechnung von Stahlbetonscheiben unter Berücksichtigung des Verbundverhaltens. Phd Thesis, Darmstadt University (1980)
Dragon, A., Mróz, Z.: A continuum model for plastic-brittle behaviour of rock and concrete. International Journal of Engineering Science 17(2) (1979)
Etse, G., Willam, K.: Fracture energy formulation for inelastic behavior of plain concrete. Journal of Engineering Mechanics ASCE 120(9), 1983–2011 (1994)
Ferrara, I., di Prisco, M.: Mode I fracture behaviour in concrete: nonlocal damage modeling. ASCE Journal of Engineering Mechanics 127(7), 678–692 (2001)
Fleck, N.A., Hutchinson, J.W.: A phenomenological theory for strain gradient effects in plasticity. Journal of Mechanics and Physics of Solids 41(12), 1825–1857 (1993)
Gatuingt, G., Pijaudier-Cabot, H.: Coupled damage and plasticity modelling in transient dynamic analysis of concrete. International Journal for Numerical and Analytical Methods in Geomechanics 26(1), 1–24 (2002)
Geers, M., Peijs, T., Brekelmans, W., de Borst, R.: Experimental monitoring of strain localization and failure behaviour of composite materials. Composites Science and Technology 56(11), 1283–1290 (1996)
Geers, M.G.D.: Experimental analysis and computational modeling of damage and fracture. PhD Thesis, Eindhoven University of Technology, Eindhoven (1997)
Geers, M., de Borst, R., Brekelmans, W., Peerlings, R.: Strain-based transient-gradient damage model for failure analyses. Computer Methods in Applied Mechanics and Engineering 160(1-2), 133–154 (1998)
Grassl, P., Jirasek, M.: Damage-plastic model for concrete failure. International Journal of Solids and Structures 43(22-23), 7166–7196 (2006)
Hansen, N.R., Schreyer, H.L.: A thermodynamically consistent framework for theories of elastoplasticity coupled with damage. International Journal of Solids and Structures 31(3), 359–389 (1994)
Hansen, E., Willam, K.: A two-surface anisotropic damage-plasticity model for plane concrete. In: de Borst, R. (ed.) Procceedings Int. Conf. Fracture Mechanics of Concrete Materials, Paris, Balkema, pp. 549–556 (2001)
Haskett, M., Oehlers, D.J., Mohamed Ali, M.S.: Local and global bond characteristics of steel reinforcing bars. Engineering Structures 30(2), 376–383 (2008)
Häuβler-Combe, U., Prochtel, P.: Ein dreiaxiale Stoffgesetz fur Betone mit normalen und hoher Festigkeit. Beton- und Stahlbetonbau 100(1), 56–62 (2005)
Hentz, S., Donze, F.V., Daudeville, L.: Discrete element modelling of concrete submitted to dynamic loading at high strain rates. Computers and Structures 82(29-30), 2509–2524 (2004)
Herrmann, H.J., Hansen, A., Roux, S.: Fracture of disordered elastic lattices in two dimensions. Physical Review B 39(1), 637–647 (1989)
Hillerborg, A., Modeer, M., Peterson, P.E.: Analysis of crack propagation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Concr. Res. 6, 773–782 (1976)
Hillerborg, A.: The theoretical basis of a method to determine the fracture energy of concrete. Materials and Structures 18(1), 291–296 (1985)
Hordijk, D.A.: Local approach to fatigue of concrete, PhD dissertation, Delft University of Technology (1991)
Hsieh, S.S., Ting, E.C., Chen, W.F.: Plasticity-fracture model for concrete. International Journal of Solids and Structures 18(3), 181–187 (1982)
Huerta, A., Rodriguez-Ferran, A., Morata, I.: Efficient and reliable non-local damage models. In: Kolymbas, D. (ed.). Lecture Notes in Applied and Computational Mechanics, vol. 13, pp. 239–268. Springer, Heidelberg (2003)
Hughes, T.J.R., Winget, J.: Finite Rotation Effects in Numerical Integration of Rate Constitutive Equations Arising in Large Deformation Analysis. International Journal for Numerical Methods in Engineering 15(12), 1862–1867 (1980)
Ibrahimbegovic, A., Markovic, D., Gatuing, F.: Constitutive model of coupled damage-plasticity and its finite element implementatation. Revue Européenne des Eléments Finis 12(4), 381–405 (2003)
Jirasek, M., Zimmermann, T.: Analysis of rotating crack model. ASCE Journal of Engineering Mechanics 124(8), 842–851 (1998)
Jirasek, M.: Nonlocal models for damage and fracture: comparison of approaches. International Journal of Solids and Structures 35(31-32), 4133–4145 (1998)
Jirasek, M.: Comments on microplane theory. In: Pijaudier-Cabot, G., Bittnar, Z., Gerard, B. (eds.) Mechanics of Quasi-Brittle Materials and Structures, pp. 55–77. Hermes Science Publications (1999)
Jirasek, M., Rolshoven, S.: Comparison of integral-type nonlocal plasticity models for strain-softening materials. International Journal of Engineering Science 41(13-14), 1553–1602 (2003)
Jirasek, M.: Non-local damage mechanics with application to concrete. In: Vardoulakis, I., Mira, P. (eds.) Failure, Degradation and Instabilities in Geomaterials, Lavoisier, pp. 683–709 (2004a)
Jirasek, M., Rolshoven, S., Grassl, P.: Size effect on fracture energy induced by non-locality. International Journal for Numerical and Analytical Methods in Geomechanics 28(7-8), 653–670 (2004b)
Jirasek, M., Marfia, S.: Non-local damage model based on displacement averaging. International Journal for Numerical Methods in Engineering 63(1), 77–102 (2005)
Karsan, D., Jirsa, J.O.: Behavior of concrete under compressive loadings. Journal of the Structural Division (ASCE) 95(12), 2543–2563 (1969)
Katchanov, L.M.: Introduction to continuum damage mechanics. Martimus Nijhoff, Dordrecht (1986)
Khoei, A.R., Bakhshiani, A., Mofid, M.: An implicit algorithm for hypoelasto-plastic and hypoelasto-viscoplastic endochronic theory in finite strain isotropic–kinematic-hardening model. International Journal of Solids and Structures 40(13-14), 3393–3423 (2003)
Klisiński, M., Mróz, Z.: Description of non-elastic deformation and damage of concrete. Script, Technical University of Poznan, Poznan (1988) (in polish)
Kozicki, J., Tejchman, J.: Effect of aggregate structure on fracture process in concrete using 2D lattice model. Archives of Mechanics 59(4-5), 1–20 (2007)
Krajcinovic, D., Fonseka, G.U.: The continuous damage theory of brittle materials. Journal of Applied Mechanics ASME 48(4), 809–824 (1981)
Kuhl, E., Ramm, E.: Simulation of strain localization with gradient enhanced damage models. Computational Material Sciences 16(1-4), 176–185 (2000)
Lade, P.V., Jakobsen, K.P.: Incrementalization of a single hardening constitutive model for frictional materials. International Journal for Numerical and Analytical Methods in Geomechanics 26(7), 647–659 (2002)
Le Bellego, C., Dube, J.F., Pijaudier-Cabot, G., Gerard, B.: Calibration of nonlocal damage model from size effect tests. European Journal of Mechanics A/Solids 22(1), 33–46 (2003)
Lee, J., Fenves, G.L.: Plastic-damage model for cyclic loading of concrete structures. Journal of Engineering Mechanics 124(8), 892–900 (1998a)
Lee, J., Fenves, G.L.: A plastic-damage concrete model for earthquake analysis of dams. Earthquake Engng. and Struct. Dyn. 27, 937–956 (1998b)
Lemaitre, J.: Coupled elasto-plasticity and damage constitutive equations. Computer Methods in Applied Mechanics and Engineering 51(1-3), 31–49 (1985)
Lemaitre, J., Chaboche, J.L.: Mechanics of solid materials. Cambridge University Press, Cambridge (1990)
Lodygowski, T., Perzyna, P.: Numerical modelling of localized fracture of inelastic solids in dynamic loading process. International Journal for Numerical Methods in Engineering 40(22), 4137–4158 (1997)
Loret, B., Prevost, J.H.: Dynamic strain localisation in elasto-visco-plastic solids, Part 1. General formulation and one-dimensional examples. Computer Methods in Applied Mechanics and Engineering 83(3), 247–273 (1990)
Lubliner, J., Oliver, J., Oller, S., Onate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 229–326 (1989)
Majewski, T., Bobinski, J., Tejchman, J.: FE-analysis of failure behaviour of reinforced concrete columns under eccentric compression. Engineering Structures 30(2), 300–317 (2008)
Mahnken, T., Kuhl, E.: Parameter identification of gradient enhanced damage models. European Journal of Mechanics - A/Solids 18(5), 819–835 (1999)
Maier, T.: Numerische Modellierung der Entfestigung im Rahmen der Hypoplastizität. PhD Thesis, University of Dortmund (2002)
Maier, T.: Nonlocal modelling of softening in hypoplasticity. Computers and Geotechnics 30(7), 599–610 (2003)
Marcher, T., Vermeer, P.A.: Macro-modelling of softening in non-cohesive soils. In: Vermeer, P.A., et al. (eds.) Continuous and Discontinuous Modelling of Cohesive-Frictional Materials, pp. 89–110. Springer, Heidelberg (2001)
Marzec, I., Bobinski, J., Tejchman, J.: Simulations of crack spacing in reinforced concrete beams using elastic-plasticity and damage with non-local softening. Computers and Concrete 4(5), 377–403 (2007)
Marzec, I.: Application of coupled elasto-plastic-damage models with non-local softening to concrete cyclic behavior. PhD Thesis, Gdańsk University of Technology (2009)
Marzec, I., Tejchman, J.: Modeling of concrete behavior under cyclic loading using different coupled elasto-plastic-damage models with non-local softening. In: Oñate, E., Owen, D.R.J. (eds.) X International Conference on Computational Plasticity COMPLAS X, pp. 1–4. CIMNE, Barcelona (2009)
Marzec, I., Tejchman, J.: Enhanced coupled elasto-plastic-damage models to describe concrete behaviour in cyclic laboratory tests. Archives of Mechanics (2011) (in print)
Mazars, J.: A description of micro- and macro-scale damage of concrete structures. Engineering Fracture Mechanics 25(5-6), 729–737 (1986)
Mazars, J., Pijaudier-Cabot: Continuum damage theory – applications to concrete. Journal of Engineering Mechanics ASCE 115(2), 345–365 (1989)
Meftah, F., Reynouard, J.M.: A multilayered mixed beam element on gradient plasticity for the analysis of localized failure modes. Mechanics of Cohesive-Frictional Materials 3(4), 305–322 (1998)
Menetrey, P., Willam, K.J.: Triaxial failure criterion for concrete and its generalization. ACI Structural Journal 92(3), 311–318 (1995)
Menzel, A., Steinmann, P.: On the continuum formulation of higher gradient plasticity for single and polycrystals. Journal of the Mechanics and Physics of Solids 48(8), 1777–1796 (2000)
Meschke, G., Lackner, R., Mang, H.A.: An anisotropic elastoplastic-damage model for plain concrete. International Journal for Numerical Methods in Engineering 42(4), 702–727 (1998)
Moonen, P., Carmeliet, J., Sluys, L.J.: A continuous-discontinuous approach to simulate fracture processes. Philosophical Magazine 88(28-29), 3281–3298 (2008)
Mühlhaus, H.-B.: Scherfugenanalyse bei Granularen Material im Rahmen der Cosserat-Theorie. Ingen. Archiv. 56, 389–399 (1986)
Mühlhaus, H.B., Aifantis, E.C.: A variational principle for gradient plasticity. International Journal of Solids and Structures 28(7), 845–858 (1991)
Needleman, A.: A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics 54(3), 525–531 (1987)
Needleman, A.: Material rate dependence and mesh sensitivity in localization problems. Computer Methods in Applied Mechanics and Engineering 67(1), 69–85 (1988)
Nguyen, G.D.: A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory, PhD Thesis, Trinity College, University of Oxford (2005)
Nguyen, G.D.: A thermodynamic approach to non-local damage modelling of concrete. International Journal of Solids and Structures 45(7-8), 1918–1932 (2008)
Oliver, J., Huespe, A.E., Sanchez, P.J.: A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM. Computer Methods in Applied Mechanics and Engineering 195(37-40), 4732–4752 (2006)
Ortiz, M., Simo, I.C.: An analysis of a new class of integration algorithms for elastoplastic constitutive relation. International Journal for Numerical Methods in Engineering 23(3), 353–366 (1986)
Ortiz, M., Pandolfi, A.: Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. International Journal for Numerical Methods in Engineering 44(9), 1267–1282 (1999)
Ottosen, N.S.: A failure criterion for concrete. Journal of Engineering Mechanics Division ASCE 103(4), 527–535 (1977)
Ozbolt, J.: Maβstabseffekt und Duktulität von Beton- und Stahlbetonkonstruktionen. Habilitation, Universität Stuttgart (1995)
Palaniswamy, R., Shah, S.P.: Fracture and stress-strain relationship of concrete under triaxial compression. Journal of the Structural Division (ASCE) 100(ST5), 901–916 (1974)
Pamin, J.: Gradient-dependent plasticity in numerical simulation of localization phenomena. PhD Thesis, University of Delft (1994)
Pamin, J., de Borst, R.: Simulation of crack spacing using a reinforced concrete model with an internal length parameter. Arch. App. Mech. 68(9), 613–625 (1998)
Pamin, J., de Borst, R.: Stiffness degradation in gradient-dependent coupled damage-plasticity. Archives of Mechanics 51(3-4), 419–446 (1999)
Pamin, J.: Gradient-enchanced continuum models: formulation, discretization and applications. Habilitation, Cracow University of Technology, Cracow (2004)
Pedersen, R.R., Simone, A., Sluys, L.J.: An analysis of dynamic fracture in concrete with a continuum visco-elastic visco-plastic damage model. Engineering Fracture Mechanics 75(13), 3782–3805 (2008)
Peerlings, R.H.J., de Borst, R., Brekelmans, W.A.M., Geers, M.G.D.: Gradient enhanced damage modelling of concrete fracture. Mechanics of Cohesive-Frictional Materials 3(4), 323–342 (1998)
Perdikaris, P.C., Romeo, A.: Size effect on fracture energy of concrete and stability issues in three-point bending fracture toughness testing. ACI Materials Journal 92(5), 483–496 (1995)
Pietruszczak, D., Jiang, J., Mirza, F.A.: An elastoplastic constitutive model for concrete. International Journal of Solids and Structures 24(7), 705–722 (1988)
Pijaudier-Cabot, G., Bazant, Z.P.: Nonlocal damage theory. Journal of Engineering Mechanics ASCE 113(10), 1512–1533 (1987)
Pijaudier-Cabot, G.: Non-local damage. In: Mühlhaus, H.-B. (ed.) Continuum Models for Materials and Microstructure, pp. 107–143. John Wiley & Sons Ltd. (1995)
Pijaudier-Cabot, G., Haidar, K., Loukili, A., Omar, M.: Ageing and durability of concrete structures. In: Darve, F., Vardoulakis, I. (eds.) Degradation and Instabilities in Geomaterials, Springer, Heidelberg (2004)
Polizzotto, C., Borino, G., Fuschi, P.: A thermodynamically consistent formulation of nonlocal and gradient plasticity. Mechanics Research Communications 25(1), 75–82 (1998)
Polizzotto, C., Borino, G.: A thermodynamics-based formulation of gradient-dependent plasticity. Eur. J. Mech. A/Solids 17, 741–761 (1998)
Polizzotto, C.: Remarks on some aspects of non-local theories in solid mechanics. In: Proc. 6th National Congr. SIMAI, Chia Laguna, Italy, CD-ROM (2002)
Pramono, E.: Numerical simulation of distributed and localised failure in concrete. PhD Thesis, University of Colorado-Boulder (1988)
Pramono, E., Willam, K.: Fracture energy-based plasticity formulation of plain concrete. Journal of Engineering Mechanics ASCE 115(6), 1183–1204 (1989)
Ragueneau, F., Borderie, C., Mazars, J.: Damage model for concrete-like materials coupling cracking and friction. International Journal for Numerical and Analytical Methods in Geomechanics 5(8), 607–625 (2000)
Rashid, Y.R.: Analysis of prestressed concrete pressure vessels. Nuclear Engineering and Design 7(4), 334–344 (1968)
Reinhardt, H.W., Cornelissen, H.A.W., Hordijk, D.A.: Tensile tests and failure analysis of concrete. Journal of Structural Engineering ASCE 112(11), 2462–2477 (1986)
Rolshoven, S.: Nonlocal plasticity models for localized failure. PhD Thesis, École Polytechnique Fédérale de Lausanne (2003)
Rots, J.G.: Computational modeling of concrete fracture. PhD Thesis, Delft University (1988)
Rots, J.G., Blaauwendraad, J.: Crack models for concrete, discrete or smeared? Fixed, Multi-directional or rotating? Heron 34(1), 1–59 (1989)
Sakaguchi, H., Mühlhaus, H.B.: Mesh free modelling of failure and localisation in brittle materials. In: Asaoka, A., Adachi, T., Oka, F. (eds.) Deformation and Progressive Failure in Geomechanics, pp. 15–21 (1997)
Salari, M.R., Saeb, S., Willam, K., Patchet, S.J., Carrasco, R.C.: A coupled elastoplastic damage model for geomaterials. Computers Methods in Applied Mechanics and Engineering 193(27-29), 2625–2643 (2004)
Schlangen, E., Garboczi, E.J.: Fracture simulations of concrete using lattice models: computational aspects. Engineering Fracture Mechanics 57, 319–332 (1997)
Simo, J.C., Ju, J.W.: Strain- and stress-based continuum damage models. Parts I and II. International Journal of Solids and Structures 23(7), 821–869 (1987)
Simone, A., Sluys, L.J.: The use of displacement discontinuities in a rate-dependent medium. Computer Methods in Applied Mechanics and Engineering 193(27-29), 3015–3033 (2004)
Skarżyński, L., Tejchman, J.: Mesoscopic modelling of strain localization in concrete. Archives of Civil Engineering LV(4), 521–540 (2009)
Skarżynski, L., Syroka, E., Tejchman, J.: Measurements and calculations of the width of the fracture process zones on the surface of notched concrete beams. Strain 47(s1), 319–322 (2011)
Simone, A., Wells, G.N., Sluys, L.J.: Discontinuous Modelling of Crack Propagation in a Gradient Enhanced Continuum. In: Proc. of the Fifth World Congress on Computational Mechanics WCCM V, Vienna, CDROM (2002)
Sluys, L.J.: Wave propagation, localisation and dispersion in softening solids, PhD thesis, Delft University of Technology, Delft (1992)
Sluys, L.J., de Borst, R.: Dispersive properties of gradient and rate-dependent media. Mechanics of Materials 18(2), 131–149 (1994)
Strömberg, L., Ristinmaa, M.: FE-formulation of nonlocal plasticity theory. Computer Methods in Applied Mechanics and Engineering 136(1-2), 127–144 (1996)
Syroka, E.: Investigations of size effects in reinforced concrete elements. Phd Thesis (2011) (under preparation)
Tejchman, J., Wu, W.: Numerical study on patterning of shear bands in a Cosserat continuum. Acta Mechanica 99(1-4), 61–74 (1993)
Tejchman, J., Herle, I., Wehr, J.: FE-studies on the influence of initial void ratio, pressure level and mean grain diameter on shear localisation. International Journal for Numerical and Analitycal Methods in Geomechanics 23(15), 2045–2074 (1999)
Tejchman, J.: Influence of a characteristic length on shear zone formation in hypoplasticity with different enhancements. Computers and Geotechnics 31(8), 595–611 (2004)
Widulinski, L., Tejchman, J., Kozicki, J., Leśniewska, D.: Discrete simulations of shear zone patterning in sand in earth pressure problems of a retaining wall. International Journal of Solids and Structures 48(7-8), 1191–1209 (2011)
Willam, K.J., Warnke, E.P.: Constitutive model for the triaxial behaviour of concrete. In: IABSE Seminar on Concrete Structures Subjected to Triaxial Stress, Bergamo, Italy, pp. 1–31 (1975)
Willam, K., Pramono, E., Sture, S.: Fundamental issues of smeared crack models. In: Proceedings SEM/RILEM International Conference of Fracture of Concrete and Rock (1986)
Winnicki, A., Pearce, C.J., Bicanic, N.: Viscoplastic Hoffman consistency model for concrete. Computers and Structures 79(1), 7–19 (2001)
Winnicki, A.: Viscoplastic and internal discontinuity models in analysis of structural concrete. Habilitation, University of Cracow (2009)
Vardoulakis, I., Aifantis, E.C.: A gradient flow theory of plasticity for granular materials. Acta Mechanica 87(3-4), 197–217 (1991)
Vervuurt, A., van Mier, J.G.M., Schlangen, E.: Lattice model for analyzing steel-concrete interactions. In: Siriwardane, Zaman (eds.) Comp. Methods and Advances in Geomechanics, Balkema, Rotterdam, pp. 713–718 (1994)
Voyiadjis, G.Z., Taqieddin, Z.N., Kattan, P.: Theoretical Formulation of a Coupled Elastic-Plastic Anisotropic Damage Model for Concrete using the Strain Energy Equivalence Concept. International Journal of Damage Mechanics 18(7), 603–638 (2009)
Zbib, H.M., Aifantis, C.E.: A gradient dependent flow theory of plasticity: application to metal and soil instabilities. Applied Mechanics Reviews 42(11), 295–304 (1989)
Zervos, Z., Papanastasiou, P., Vardoulakis, I.: A finite element displacement formulation for gradient plasticity. International Journal for Numerical Methods in Engineering 50(6), 1369–1388 (2001)
Zhou, W., Zhao, J., Liu, Y., Yang, Q.: Simulation of localization failure with strain-gradient-enhanced damage mechanics. International Journal for Numerical and Analytical Methods in Geomechanics 26(8), 793–813 (2002)
Zhou, F., Molinari, J.F.: Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency. International Journal for Numerical Methods in Engineering 59(1), 1–24 (2004)
Yang, Z., Xu, X.F.: A heterogeneous cohesive model for quasi-brittle materials considering spatially varying random fracture properties. Computer Methods in Applied Mechanics and Engineering 197, 4027–4039 (2008)
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Tejchman, J., Bobiński, J. (2013). Continuous Approach to Concrete. In: Continuous and Discontinuous Modelling of Fracture in Concrete Using FEM. Springer Series in Geomechanics and Geoengineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28463-2_3
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