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The deep drawing of an aluminum alloy used in the packaging industry for the beverage can manufacturing process is investigated. In this work, the effective constitutive behavior is based on a crystal plasticity model in combination with a non-linear Hashin-Shtrikman type homogenization scheme in which a reference stiffness controls the stress and strain fluctuations. The simulation results are compared to experiments in terms of deep drawing earing profiles, texture evolution, and localization.