Keywords: constitutive, concrete, plastic, damage, finite element, micro-mechanics.

A review of work on the finite element analysis of concrete structures over the last forty years is presented. The paper concentrates mainly on constitutive modelling and in particular on models which use plasticity, damage, plastic-damage and micromechanical theories but also considers computational issues such as mesh dependency and mesh bias and the need to regularise solutions. Methods for regularising solutions such as the Bazant-Oh [1] crack band model and integral and gradient non-local approaches are also discussed.

The paper touches on the first work undertaken on total stress-strain theories and highlights the inadequacy of such an approach to capture the complex mechanical behaviour of concrete. However, the value of the experimental work undertaken to support these early models is emphasised.

Plasticity models are then considered including the early contribution of Willam [2] as well as more recent and comprehensive models. This is followed by a consideration of damage mechanics and a discussion of its appeal as a method for modelling concrete fracture. A representative model for concrete developed by Mazaars and Pijaudier-Cabot [3] is described along with other more recent contributions to this field.

A significant part of the review is devoted to plastic-fracture and plastic-damage models. It is emphasised that both damage and plasticity are needed in an effective macro-scopic model for concrete. The model of Owen et al. [4] is used to represent a typical plastic-directional fracture model of the 1980s and the stages towards the development of more recent plastic-damage models such as that developed by the author [5] and that of Nguyen, and Korsunsky [6] are traced. The strengths and weaknesses of plastic-fracture and plastic-damage approaches are highlighted and this moves the review to a discussion of methods for dealing with mesh-dependent behaviour of strain softening models. The Crack-band model of Bazant and Oh [1] is discussed first and this is followed by a review of integral [7] and gradient [8] non-local theories, including more recent contributions in this area.

The review then continues with a discussion of more micro-mechanical models, for example that due to Pensé et al. [9], and also touches upon multi-scale models. The final brief review section considers the role of strong-discontinuity models in simulating concrete fracture.

The closing discussion looks to the future and points to the elements of models which the author believes will provide the ultimate solution to the accurate and robust simulation of concrete structures.

[1]

Z.P. Bazant, B.H. Oh, "Crack band theory for fracture in concrete", Materials and Structures, 16, 155-177, 1983. doi:10.1007/BF02486267

[2]

K.J. Willam, E.P. Warnke, "Constitutive models for triaxial behavior of concrete", Proc. Int. Assoc. Bridge Struct. Engrg, Report 19, Zurich, Switzerland, 1-30, 1975.

[3]

J. Mazars, G. Pijaudier-Cabot, "Continuum damage theory – application to concrete", Journal of Engineering Mechanics, 115(2), 345-365, 1989. doi:10.1061/(ASCE)0733-9399(1989)115:2(345)

[4]

D.R.J. Owen, J.A. Figeiras, F. Damjanic, "Finite element analysis of reinforced and prestressed concrete structures including thermal loading", Comput. Meth. Appl. Mech. Engng., 41, 323-366, 1983. doi:10.1016/0045-7825(83)90012-9

[5]

A.D. Jefferson, "Craft - a plastic-damage-contact model for concrete. I. Model theory and thermodynamic considerations", International Journal of Solids and Structures, 40(22), 5973-5999, 2003. doi:10.1016/S0020-7683(03)00390-1

[6]

G.D. Nguyen, A.M. Korsunsky, "Development of an approach to constitutive modelling of concrete: Isotropic damage coupled with plasticity", International Journal of Solids and Structures, 45, 5483–5501, 2008. doi:10.1016/j.ijsolstr.2008.05.029

[7]

G. Pijaudier-Cabot, Z.P. Bazant, "Non-local damage theory", ASCE Journal of Engineering Mechanics, 113(10), 1512-1533, 1987. doi:10.1061/(ASCE)0733-9399(1987)113:10(1512)

[8]

R.H.J. Peerlings, R. de Borst, W.A.M. Brekelmans, J.H.P. de Vree, "Gradient enhanced damage for quasi-brittle materials", International Journal for Numerical Methods in Engineering, 39(19), 3391–3403, 1996. doi:10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D

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