Statistical aspects of the identification of material parameters for elasto-plastic models |
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Authors: | R Kreißig U Benedix U-J Görke |
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Institution: | (1) Institute of Mechanics, Chemnitz University of Technology, Str. der Nationen 62, D-09111 Chemnitz, Germany, DE |
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Abstract: | Summary The presented method to identify material parameters for inelastic deformation laws is based on the numerical analysis of
inhomogeneous stress and strain fields received from suitable experiments. Tensile and bending tests were carried out to obtain
elastic and hardening parameters. The deformation law for small elasto-plastic strains is presented as a system of nonlinear
differential and algebraic equations (DAE) consisting of the stress–strain relation, evolution equations for the internal
variables and the yield condition. Different rules for the evolution equations of isotropic, kinematic and distorsional hardening
are proposed. The DAE are discretized using an implicit Euler method, and the resulting system of nonlinear algebraic equations
is solved using the Newton method. Deterministic optimization procedures are preferred to identify material parameters from
a least-squares functional of numerical and measured comparative quantities. The gradient of the objective function was calculated
using a semianalytical sensitivity analysis. Due to measurement errors, the optimal sets of material parameters are non unique.
The approximate estimation of confidence regions and the calculation of correlation coefficients is presented.
The results of several optimization processes for material parameters of elasto-plastic deformation laws show a good agreement
between measured and calculated values, but they show also problems which may occur if systematic errors will not be recognized
and deleted.
Received 30 September 1999; accepted for publication 8 March 2000 |
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Keywords: | Plasticity small strains optimization sensitivity analysis statistics |
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