On the identifiability of Anand visco-plastic model parameters using the Virtual Fields Method

In this paper, the issue of the identification of constitutive parameters of the Anand visco-plastic model is addressed using the Virtual Fields Method (VFM) in an infinitesimal deformation framework. By using VFM, one can take advantage of heterogeneous strain fields obtained by full-field experimental techniques, such as Digital Image Correlation (DIC). Since a wide range of strains and strain rates are sampled in a typical heterogeneous strain field, the number of experiments required to reliably estimate constitutive parameters, especially of rate-dependent materials, is significantly smaller than that needed if conventional experiments (such as uniaxial tension or pure shear configurations) leading to nominally homogeneous strain states were used. However, for such an approach to be successful, the test configuration and loading program should be such that all the constitutive parameters play a significant role (are 'activated') in the resulting strain fields. An analysis of the Anand constitutive model shows that 4 of the 8 parameters can only be found to within a multiplicative constant from full-field kinematic data. Therefore, one of these 4 constants is arbitrarily chosen and the activation of the remaining 7 material parameters is investigated by performing a series of one-element models. Detailed sensitivities of the VFM cost function to these material parameters are derived for a variety of normal stress to shear stress ratios and loading rates. Two main conclusions are drawn based on this one-element study: (i) the VFM cost function sensitivities to the material parameters do not vary significantly with loading ratios or rates, and (ii) 2 of the 7 material parameters are not activated for any of the loading ratios or rates considered. Based on the results of the finite-element study, a modified single lap-shear test configuration is designed to yield heterogeneous strains in the joint. Deformation data from a finite-element analysis of this experiment are used as inputs to a VFM routine to compute the Anand material parameters. Our results highlight that non-uniqueness of the identified parameters is a significant issue. The effect of the choice of the cost function and the loading profile on the inverse technique is also thoroughly investigated.