Sample shapes for reliable parameter identification in elasto-plasticity
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O R I G I NA L PA P E R
A. V. Shutov
· A. A. Kaygorodtseva
Sample shapes for reliable parameter identification in elasto-plasticity
Received: 27 February 2020 / Revised: 10 June 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract Phenomenological constitutive equations contain material parameters which cannot be measured directly in the experiment. We address the problem of error-resistant parameter identification for models of large strain elasto-plasticity. The identification is based on tests with a heterogeneous stress state. A methodology is presented which allows us to assess the reliability of identification strategies in terms of their sensitivity to measurement errors. A vital part of the methodology is the mechanics-based metric in the space of material parameters. The measure of sensitivity is the size of a parameter cloud, computed using this metric. Efficient procedures of Monte Carlo type for computation of the parameter cloud are presented and discussed. The methodology is exemplified in terms of a model with combined nonlinear isotropic-kinematic hardening. First, for an aluminum alloy, non-monotonic torsion tests with different sample cross sections are analyzed. Second, for the identification of hardening parameters of steel, three different tension–compression samples are considered. In both examples, various combinations of tests are checked for sensitivity to measurement errors identifying best and worst combinations.
1 Introduction Although substantial progress has been made in the field of physics-based material modeling [7,17], purely phenomenological (macroscopic) models are widely used in various applications [6]. The advantage of such phenomenological models lies in their high computational efficiency. However, the price for the high accuracy and efficiency is a large number of material parameters which enter the constitutive equations. Moreover, even some physics-based models rely on phenomenological assumptions, formulated on lower length scales [17]. In any case, one needs to identify the unknown material parameters using actual experimental data. A special aspect of this study is the sensitivity of the identified material parameters with respect to noise inevitably contained in the experimental data. Therefore, the parameter identification is carried out in a stochastic context, where experimental results are random variables; various stochastic models for experimental measurements are found in [4,22,28]. Following the ideas from [4], we assume that the random noise is additively superimposed with the measurement results. Monte Carlo simulation allows us to estimate the sensitivity of the parameters with respect to the noise. Low sensitivity is understood as stability; stable identification strategies can be used in practice. On the other hand, high sensitivity means that a very small experimental error may cause a substantial change in material parameters. Such unstable procedures typically arise in case of insufA. V. Shutov (B) · A. A. Kaygorodtseva Lavr
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