Keywords: identification, inverse analysis, global optimisation, sensitivity analysis, ductile damage, global measurement, Lemaitre damage.

Identification of material parameters is important to improve the accuracy of finite element computations. Some joining processes such as riveting or clinching are based on the material plastic deformation ability [1]. The mechanical strength of these joining points is linked to the yield and damage history of materials during the joining process. To predict the final mechanical strength of the assembly, reliable damage parameters are important.

An elastic-plastic behaviour coupled with the Lemaitre ductile damage model is chosen to describe the mechanical behaviour of steel [2]. To identify Lemaitre damage parameters, local or global measurements can be used. Using global data allows the non standardized test to be performed. These measures, local or global, are then used in an inverse analysis procedure. Our study aims at working on global measurements resulting from tensile tests.

To illustrate the methodology, the sensitivity analysis focuses on only two parameters of the Lemaitre damage model. The simulation of the tensile test is carried out using the finite element library CIMLibR. The numerical load-displacement curve is compared to a virtual experimental curve by means of a least square function in order to compute an adapted objective function. One-hundred and twenty-one simulations are preformed to build a landscape view of the objective function. This landscape gives interesting information to calibrate the inverse analysis procedure: the landscape shows that the minimisation problem has multiple optima (two in this case), and weak gradient area.

Sensitivity analysis leads to use an advanced optimisation procedure in order to identify damage parameters. The efficient global optimization (EGO) algorithm is used [3]. This algorithm deals with an iterative updating kriging meta-model. We managed to use a meta-model assisted method in order to limit the computation time. Optimisation tests show that an optimal solution is found after forty objective function exact evaluations: the two local minimums are explored.

This calibration enables the identification of damage parameters on experimental results. Here a HLE S355MC steel is tested. The identification procedure gives an accurate result: the final objective function is equal to 3e^-4.

Sensitivity analysis allowed the calibration of the identification procedure. It has also shown some area with weak gradients, and multiple minimums. One way to solve this problem could be to deal with more rich experimental data obtained from field measurements.

1

P.O. Bouchard, T. Laurent, L. Tollier, "Numerical modelling of self-pierce riveting from riveting process modelling down to structural analysis", J. Mater. Process. Technol., 200, 290-300, 2008. doi:10.1016/j.jmatprotec.2007.08.077

2

J. Lemaitre, "A course on damage mechanics", Springer-Verlag (second edition), 1996.

3

D.R. Jones, M. Schonlau, W.J. Welch, "Efficient Global Optimization of expensive black-box functions", Journal of global optimization, 13, 455-492, 1998. doi:10.1023/A:1008306431147

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