Keywords: nonlinear modelling, damage mechanics, concrete, multi-axial stess, damage modulus, calibration, energy release rate.

In recent years, considerable research has focused on the modelling of the mechanical behaviour of concrete using damage mechanics (CDM) approach. These models vary widely in complexity, ranging from the simple one-parameter model for simulating isotropic damage to that of the four-parameter model depicting the anisotropic damage

These models aim at predicting the nonlinear behaviour of concrete in general due to progressive degradation of the mechanical properties leading to stiffness degradation, strain softening, and volumetric dilatation

The development of a complete incremental theory of damage requires the integration of components that include stress-stain relationships, thermo dynamic laws governing damage in terms of strain energy release vectors and the damage evolution laws. The concept of the effective damage tensor along with the bounding surfaces approach controlling the tensorial-damage rate is adopted in [1,2]

In previous work the author has developed a damage based computational model for concrete which predicts well the concrete response in the pre-peak regime and yet not much correlation between experimental values and the predicted ones in the post-peak range (i.e. in the softening range) [3,4]. It has been found that the problem lies in the adopted specific form of the damage modulus, which does not allow for the gradual growth of damage thereby rendering the material to behave in an elastic- rigid manner

The present study is aimed toward the refinement of an anisotropic damage mode capable of predicting compressive behaviour for a range of concrete strengths through the adaptation of the constitutive model developed by the author for the case of monotonic loading. The proposed model in which an innovative functional form for the damage modulus is capable of predicting a wide range of concrete strength with emphasis to predicting the post-peak behaviour is investigated

An introduction of a new material parameter in the damage modulus has proven that the post-peak response can be simulated for concrete strengths ranging from psi

The predicted results correlate well with the available experimental data including high strength concrete lacking ductility. The simulative capability of the model to capture the response of concrete is reflected through the stress-strain curves and the evolution of the damage-induced energy release rate versus the accumulated damage. The formulation has been expressed in a form adoptable for inclusion into a finite element coding

1

W. Suaris, S.P. Shah,"A rate sensitive damage theory for brittle solids", Journal of Engg. Mech, ASCE, 110(6), 985-997, 1984. doi:10.1061/(ASCE)0733-9399(1984)110:6(985)

2

G.Z. Voyiadjis, T.M. Abu-Lebdeh, "Damage model for concrete using bounding surface concept", Journal of Engg. Mech, ASCE, 119(9), 1865-1885, 1993. doi:10.1061/(ASCE)0733-9399(1993)119:9(1865)

3

A.R. Khan, A.H. Al-Gadhib, M.H. Baluch, "Three parameter damage model for concrete", Proceeding of the Fifth International Conference on Computational Structures Technology, Leuven,Belgium, 95-106, 2000.

4

A.H. Al-Gadhib, M.H. Baluch, A. Shaalan, A.R. Khan, "Damage model for monotonic & fatigue response of high strength concrete", Journal of Damage Mechanics, 9, 57-78, 2000. doi:10.1177/105678950000900105

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