Application of canonical correlation analysis to a sensitivity study of constitutive model parameter fitting

Publication date: 15 October 2017
Source:Materials & Design, Volume 132
Author(s): Sudipto Mandal, Brian T. Gockel, Anthony D. Rollett
Successful modeling of a material's deformation behavior is dependent on the development of realistic constitutive models that can mimic the actual response of the material of interest. In-depth knowledge about the parameters in a constitutive model will lead to a better understanding of the relationship between flow stress and deformation conditions and will eventually aid in better design of the deformation process. Curve-fitting is generally employed to calibrate constitutive models using experimental data. However, the relative impact of constitutive model parameters on the mechanical response for different models has not been extensively explored. In this study, both local and global sensitivity analysis methods are used to understand and quantify the contribution of the parameters. Canonical correlation analysis (CCA) has been used to understand the effect of constitutive model parameters on the flow stress behavior of titanium alloys. This analysis has been performed for the Mechanical Threshold Stress (MTS) model, which is a constitutive description based on the physics of dislocation motion. The limitations of local sensitivity methods have been highlighted and it has been shown that CCA provides a measure of both an individual variable's contribution and the effectiveness of the parameter set as a whole.

Graphical abstract

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