Keywords: parameter identification, inverse problem, damage model, cracks, radial basis function network.

During the tensile test and the three-point bending test, a concrete specimen is damaged by cracking. Brancherie and Ibrahimbegovic [1] developed a simple model capable of describing the behaviour of specimen weakened by distributed as well as macroscopic cracks. One important advantage of this model is the very small dependence of its precision on the density of a finite element mesh. The model describes the three stages of concrete behaviour during the tensile loading: elastic, plastic hardening and continuum as well as discrete softening due to damage.

A particular concrete is defined by six parameters, which are significant in the different stages of loading and it is possible to explain the geometry of the stress-strain curve for one material stage. During the tensile test, the homogeneous strain field becomes distorted after the spring of the crack. Therefore, the global response represented by the load-deflection curve is not exactly the same as the stress-strain curve for one material point. Nevertheless the identification of material parameters from this loading test should not be complicated. Practical realization of this loading test is, however, not trivial. It is much simpler to realize the three-point bending test. The stress field and the strain field, respectively, are heterogeneous from the start of the experiment. The macro-scale measurements provide the load-deflection curve that incorporates data from different parts of the specimen, which are in different stages of behaviour. For that reason, it is not possible to simply estimate the parameter values from the measured load-deflection curve for the three-point bending test.

In this paper, we present details of the approach to identify all of the model parameters from the simple tensile test and. The emphasis is on the choice of the appropriate measurements with a view to identify all the model parameters and the formulation of a minimization problem.

Using the two-dimensional representation of the experiments created using the software FEAP [2], several realizations of the loading test were simulated for different parameter sets. The simulated annealing method (implemented in the FREET software [3]) was used for the preparation of these sets to make these sets as much as possible distributed over the whole space defined by realistic values of each parameter. Using the simulated load-deflection curves, the stochastic sensitivity analysis using the Pearson correlation coefficient was evaluated in order to explore the evolution of the influence of particular parameters on the global response of the specimen during the loading. Results of sensitivity analysis served to formulate a balanced optimization problem.

Among the preliminary simulations, the spring of crack appeared only for 23 percent of specimens. For that reason, the sensitivity analysis showed very little influence on the parameters governing the softening stage of the global response. At the same time, the calculations of the softening stage are much more time consuming than for the elastic or hardening stage. Therefore, the sequential identification is proposed here as it is a less time demanding approach.

The identification problem is formulated as an optimization task. Because of the absence of real experimental data, one simulation is considered in the place of experimental measurements. Then the task is to minimize the difference between "measured" curves and simulated curves. To solve this optimization problem, the deterministic steepest descent method and the stochastic optimization method based on approximation using a radial basis function network developed in [4] were tested. We discuss the advantages and disadvantages of both methods.

1

A. Ibrahimbegovic, D. Brancherie, "Combined hardening and softening constitutive model of plasticity: precursor to shear slip line failure", Comp. Mechanics, 31, (2003), 88-100. doi:10.1007/s00466-002-0396-x

2

Details and downloads of a Finite Element Analysis Program (FEAP), URL.

3

D. Novák et al., FREET Feasible Reliability Engineering Efficient Tool, Program documentation, Brno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics / Cervenka Consulting, Prague, Czech Republic, 2002.

4

A. Kucerová, M. Lepš, and J. Skocek, "black-box function optimization using radial basis function networks", In B.H.V. Topping, (editor), Proceedings of Eighth International Conference on the Application of Artificial Intelligence to Civil, Structural and Environmental Engineering, paper 36 on CD-ROM, Civil-Comp Press, Stirling, United Kingdom, 2005. doi:10.4203/ccp.82.36

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