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.