Application of the virtual fields method to large strain anisotropic plasticity

Abstract

The identification of the plastic behaviour of sheet metals at severe deformation is extremely important for many industrial application such as metal forming, crashworthiness, automotive, aerospace, piping, etc. In this paper, the virtual fields method (VFM) was employed to identify the constitutive parameters of anisotropic plasticity models. The method was applied using the finite deformation theory in order to account for large strains. First the theoretical principles to implement the method are described in details, especially how to derive the stress field from the strain field. Afterwards a numerical validation was performed using the Hill48 model. Several aspects were studied with the numerical model: the effect of the used virtual fields, the minimum number of specimens required to identify the parameters, the stress distribution obtained from the specimen and its influence in the identification performance. A brief analysis on the influence of noise is also conducted. Finally a series of experiments was conducted on notched specimens of stainless steel, cut along different anisotropic directions. The displacement and strain fields were obtained by digital image correlation. Afterwards, the VFM was used to identify the parameters of the Hill48 model and the Yld2000-2D model. In this case, the Hill48 model was not able to correctly describe the material behaviour, while a rather good agreement was found with the Yld2000-2D model. The potential and the limitation of the proposed method are finally discussed.

Sensitivity-based virtual fields for the non-linear virtual fields method

“…Currently, the sensitivitybased virtual field concept is being extended to large deformation and anisotropic plasticity (Hill48, Yld2000-2D). This will be applied to tests such as presented in [14,25]. Future work also includes extending the method to dynamic loading [21] where the virtual work due to inertia will be accounted for in Eq.…”

“…Elasto-plasticity was the first type of non-linear constitutive model to be tackled [8]. The non-linear virtual fields method has since been used to study a wide range of materials such as arteries [4], rubbers [10,28,29], composites [7], and metals [12][13][14]17,25]. As a result, many different non-linear constitutive model types were considered including hyperelasticity, elasto-plasticity, visco-elasticity, and anisotropic plasticity.…”

A general linear method to evaluate the hardening behaviour of metals at large strain with full‐field measurements

“…The stress normalized tensor can be retrieved from the normalized plastic flow tensor inverting the flow rule equation. Such procedure is described in details in Mathieu, Leclerc, and Roux and Rossi and Pierronand in the Appendix for the models used in this paper. In particular, using von Mises and the associated flow rule, it becomes …”

“…Among the methods that uses this principle, the virtual fields method (VFM) is one of the most widespread and well documented. In plasticity, the first application of VFM was proposed by Grédiac and Pierron, then it was extended to large strain plasticity and used to identify the post‐necking regime and anisotropic plasticity . Another inverse method that was used in the last years to identify the plastic behaviour of materials is integrated DIC, in this case, the constitutive behaviour is coupled with the image correlation algorithm so that the displacement field and the material parameters are identified at the same time, that is, the constitutive model constraints the degrees of freedom of the displacement field.…”

Enhanced features of a constitutive equation gap identification method for heterogeneous elastoplastic behaviours

“…digital image correlation, interferometric techniques, grid methods, etc. ): the finite element model updating method (FEMU) [1][2][3][4], the reciprocity gap method (RGM) [5,6], the constitutive equation gap method (CEGM) [7][8][9], the virtual field method (VFM) [10][11][12][13][14][15][16][17][18] and the equilibrium gap method (EGM) [19,20]. An overview of these identification procedures and their applications on experimental data can be found in [21].…”