Keywords: concrete modelling, three-point bending, crack band model, smeared cracks, solution strategies.

Computational research on the non-linear static behaviour of concrete (or other quassibrittle) materials is often required today. There are numerous material models for concrete and there are also a large number of strategies for the computational analyses. It is usually important to select a computational strategy which is effective and reliable for the particular problem solved. This paper discusses the use of a direct displacement solution and a linerized arc-length method for a two-dimensional analysis of numerical models of concrete specimens. Concrete is modelled with the use of a smeared crack approach [1] and with the help of Bazant's crack band model.

The experiments presented are only a small part of a research project which is aimed at developing algorithms for an efficient determination of the input data for two-dimensional non-linear constitutive models for concrete.

The paper includes several parts. In the first part a basic review of the methods is given. In the second part there is an illustrative one-dimensional example of the use of the arc-length method. In the third part the two-dimensional analyses are discussed.

A very common approach which is used for a non-linear analysis of concrete models is the application of the Newton-Raphson method with displacement loading. It is conventient and also relatively easy to use and to implement. One of the main drawbacks is the fact that it is not easy (and in many cases it is not possible) to use a direct displacement loading on complicated models. The arc-length method is often used to solve the problem. In the Newton-Raphson method the size of a load multiplier lambda is predefined and can be modified in a dependence of the convergence speed, for example. So it is nearly impossible to manage the solution to go through the peak load and there is no rule to control the size of the lambda in the post-peak part of the load-displacement relationship. The arc-length method allows the incorporation of a dependence on the other parameters (namely it includes the relation between load lambda x R^- and the displacement r into the computation of lambda).

The constitutive law is based on an equivalent one-dimensional stress-strain relationship. The compression part of this relation is assumed to be linear. It was selected for the cases discussed because a tension softening behaviour was studied. The effects of two-dimensional stress state are included in the analysis through the computation of limits of the one-dimensional law.

Selected aspects of the application of the linearised arc-length method for one-dimensional and two-dimensional non-linear constitutive modelling of concrete specimens was discussed. The results of two-dimensional modelling were compared with the results obtained from the use of the Newton-Raphson method with displacement load. It can be noticed that the use of a basic form of arc-length metod can be possible and effective but it requires special computational approaches. The comparison of results shows that very similar results can be obtained from both mentioned computational methods. Some recommendations for the setting of the linearised arc-length method parameters in the cases discussed are also given in the paper.

1

M. Jirásek, Z.P. Bazant, "Inelastic Analysis of Structures", John Willey and Sons, Chichester, USA, 2002.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)