Keywords: reinforced concrete, bond model, tension stiffening, impact loading, memory effect, damage model.

The tension stiffening effect due to bond between reinforcing steel and concrete has a basic influence on the cracking behaviour and deflection of reinforced concrete elements in cracked stage. A realistic investigation on the stiffness of structural elements is thereby only possible, when the bond behaviour is considered properly. This is applicable to structural elements under static loading as well as to those under dynamic loading with high strain rates. In this contribution a bond model with realistic material models is presented to describe the bond behaviour of reinforced concrete elements subjected to impact loading.

In a phenomenological sense, the bond mechanisms under static loading and the experimental observation of bond characteristics under high strain rates are presented. It shows that the change of bond behaviour of deformed bars under quick tensile loading is due to the change of material properties of concrete and steel under high strain rates. The bond can be always explained by the bond mechanisms under static loading. Hence it is possible to simulate the bond behaviour under high loading rates in the same way as under static case. As such, the material models for concrete and steel in the bond model can realistically describe the material behaviour under high strain rates.

From the viewpoint of damage theory the dynamic behaviour of concrete results from the static damage evolution and the dynamic damage delay effect (memory effect). A modified concrete model based on the "fictitious crack" model (FCM) in reference [1], is presented to describe the concrete behaviour and the static damage evolution under tension. The dynamic damage model suggested in reference [2] is used, which is dependent on loading history und takes into account the memory effect of concrete. The behaviour of steel is described by a strain rate-dependent plasticity model.

A modified static bond model, which is based on the simplified stress-strain relationship of embedded reinforcing steel suggested in reference [3], is extended to the dynamic case. The tensile stress as well as the ultimate tensile strength of concrete depends on loading history, and the properties of steel rely on current strain rate. Numerical examples are given to show the application of the proposed bond model.

1

Hillerborg, A., "Analysis of one single crack", In "Fracture Mechanics of Concrete", F.H. Wittmann, (Editor), Elsevier, 223-249, 1983.

2

Eibl, J. and Schmidt-Hurtienne, B., "Strain-Rate-Sensitive Constitutive Law for Concrete", ASCE Journal of Engineering Mechanics, 125(12), 1411-1420, 1999. doi:10.1061/(ASCE)0733-9399(1999)125:12(1411)

3

CEB-FIP Model Code 90. Thomas Telford, London, 1993.

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