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CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 292
Material Parameter Identification for Damage Models with Cracks A. Kucerová^{1}, D. Brancherie^{2} and A. Ibrahimbegovic^{3}
^{1}Department of Mechanics, Faculty of Civil Engineering, Czech Technical University, Prague, Czech Republic
A. Kucerová, D. Brancherie, A. Ibrahimbegovic, "Material Parameter Identification for Damage Models with Cracks", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 292, 2006. doi:10.4203/ccp.83.292
Keywords: parameter identification, inverse problem, damage model, cracks, radial basis function network.
Summary
During the tensile test and the threepoint 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 stressstrain 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 loaddeflection curve is not exactly the same as the stressstrain 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 threepoint bending test. The stress field and the strain field, respectively, are heterogeneous from the start of the experiment. The macroscale measurements provide the loaddeflection 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 loaddeflection curve for the threepoint 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 twodimensional 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 loaddeflection 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. References
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