Finite element-based virtual fields method with pseudo-real deformation fields for identifying constitutive parameters

Abstract In this study, a novel virtual fields method (VFM) based on the finite element (FE) scheme, namely FE-VFM, is proposed as an inverse method for identifying the parameters of constitutive models. In the FE-VFM, experimentally measured full-field displacements are mapped onto FE meshes using global and local shape functions, and the internal virtual work is integrated using the Gauss quadrature rule. To validate the new method, a well-designed sensitivity study is conducted using the ideal deformation obtained from FE simulations for anisotropic linear elastic and isotropic plastic materials. In the case of anisotropic elasticity, the residuals of the internal and external virtual work are not significantly affected by the order and size of FE meshes, but the order of the numerical integration has a marginal effect on the quality of the results. Conversely, substantial impacts are obtained for the plastic case, in which the size and order of the FE meshes and the order of the numerical integration are all critical to the accuracy of identification owing to large, localized deformation. Furthermore, the concept of a pseudo-real deformation field is newly proposed as a virtual field, which improves the accuracy of the FE-VFM for optimizing the constitutive parameters of the plastic material. Finally, the inverse identification of the plastic hardening law for press-hardened steel is conducted using the FE-VFM with real experimental data. The results show that the FE-VFM can successfully reproduce the full-field displacements even with relatively low-quality full-field data if an optimum FE mesh is adopted. In addition, the simulated load–displacement curve of notch tension with FE-VFM identified hardening is in good agreement with the experimental results.