Keywords: concrete model, nonlinear analysis, finite element analysis, floor slabs.

This paper presents a simple, robust, yet realistic biaxial material model for concrete, which can be employed in modelling the nonlinear response of RC and composite floor slabs under extreme loading, including fire. The proposed model accounts for the combined effects of compressive nonlinearity, tensile crack opening and closure, as well as temperature.

In modelling the compressive nonlinear response, the proposed concrete model utilises plasticity theory with an evolving biaxial interaction surface, allowing for the pre-crushing hardening and post-crushing softening responses, where two alternative expressions for the compressive envelope are proposed. In tension, on the other hand, a smeared crack approach is employed assuming a fixed crack orientation, where initial crack formation is governed by exceeding the tensile strength in one of the principal directions. Subsequently, crack formation is also allowed in the orthogonal direction. In addition, the response to subsequent shear in the crack principal plane is governed by an elastic shear retention factor and by a strength limit, allowing for interaction between shear and the biaxial direct stresses in the crack plane. As with previous models, the post-cracking response allows for softening, which partly deals with the phenomenon of tension stiffening, but importantly controls the numerical robustness of the proposed model. However, the proposed model has an important feature of dealing with crack opening and closure, which is an essential requirement for modelling the response of slabs under elevated temperature conditions.

The above features of the new concrete model are expressed in terms of stress and strain constraints, a number of which may be active simultaneously; for example, the compressive strength constraint may be active with a tensile strength constraints or with a crack closure constraint. In view of this, a sophisticated solution procedure is proposed on the material level, which enables the determination of the biaxial stress components corresponding to a biaxial strain state, accounting for all possible stress and strain constraints. This procedure is based on a sequence of constraint satisfaction/deactivation/activation steps, which altogether present a numerically robust material model for concrete. In addition, a significant benefit of the proposed procedure is that the tangent modulus matrix arises naturally as a result of the iterative solution procedure, and hence does not require a complex analytical formulation.

The proposed concrete model and solution procedure have been implemented within ADAPTIC [1], which is used in a number of studies to verify the model accuracy as well as the sensitivity of its predictions to variations in the compressive envelope. The model is utilised by a recently developed shell element for R/C and composite floor slabs [2], where favourable comparisons against experimental results on floor slabs subject to extreme loading are obtained. In particular, the overall analytical capability incorporating the proposed concrete model is shown to be able to simulate numerically difficult problems, including those involving tensile cracking, compressive crushing as well as tensile and compressive membrane action. The numerical robustness and accuracy of the overall analytical capability are evidence of similar characteristics on the level of the proposed concrete model, which achieves such qualities while retaining simplicity in both formulation and application.

1

Izzuddin, B.A., Nonlinear Dynamic Analysis of Framed Structures, PhD Thesis, Department of Civil Engineering, Imperial College, University of London, 1991.

2

Izzuddin, B.A., Tao, X.Y., and Elghazouli, A.Y., "Nonlinear Analysis of Composite Floor Slabs with Geometric Orthotropy", Proc. 8th International Conference of Civil and Structural Engineering Computing, Eisenstadt, paper 76, Civil-Comp Press, Stirling, 2001. doi:10.4203/ccp.73.76

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