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Algorithmic formulation of constitutive model based on non-associated flow rule and its application to aluminium alloy sheets

In this article application of elasto-plastic constitutive model based on non-associated flow rule to aluminium alloy sheets is considered. In analyzed model quadratic stress function adjusted to measured Lankford parameters is considered as a plastic potential function and another quadratic stress function adjusted to measured yield stresses is considered as a yield function. Predictions of planar anisotropy for analysed model are considered for aluminium alloys Al2008-T4 and Al2090-T3. Algorithmic formulation of model that assumes non-associated flow rule and isotropic hardening is derived by application of impliciting return mapping procedure. The accuracy of developed algorithm according to flow rule and material data has been investigated by calculating iso-error maps. It has been shown that, for formulation based on non-associated flow rule, error magnitude is more pronounced if strong anisotropy is considered and that reduction of strain increment doesn't entail reduction of error magnitude.

plastic anisotropy; flow rule; numerical integration of constitutive equations; accuracy

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