On the Development and Computational Implementation of Complex Constitutive Models and Parameters’ Identification Procedures

Abstract

Nowadays, the automotive industry has focused its attention to weight reduction of the vehicles to overcome environmental restrictions. For this purpose, new materials, namely, advanced high strength steels and aluminum alloys have emerged. These materials combine good formability and ductility, with a high tensile strength due to a multi-phase structure (for the steel alloys) and reduced weight (for the aluminum alloys). As a consequence of their advanced performances, complex constitutive models are required in order to describe the various mechanical features involved. In this work, the anisotropic plastic behavior of dual-phase steels and high strength aluminum alloys is described by the non-quadratic Yld2004-18p yield criterion, combined with a mixed isotropic-nonlinear kinematic hardening law. This phenomenological model allows for an accurate description of complex anisotropy and Bauschinger effects of the materials, which are essential for a reliable prediction of deep drawing and springback results using numerical simulations. To this end, an efficient computational implementation is needed, altogether with an inverse methodology to properly identify the constitutive parameters to be used as numerical simulation input. The constitutive model is implemented in the commercial finite element code ABAQUS as a user-defined material subroutine (UMAT). A multi-stage return mapping procedure, which utilizes the control of the potential residual, is implemented to integrate the constitutive equations at any instant of time (pseudo-time), during a deformation process. Additionally, an inverse methodology is developed to identify the constitutive model parameters of the studied alloys. The identification framework is based on an interface program that links an optimization software and the commercial finite element code. This methodology compares experimental data with the respective results numerically obtained. The implemented optimization process aims to minimize an objective function, which defines the difference between experimental and numerical results using the Levenberg-Marquardt gradient-based optimization method. The proposed integrated approach is validated in a number of benchmarks in sheet metal forming, including monotonic and cyclic loading, with the goal to infer about the modelling of anisotropic effects.