Constitutive modeling of sheet metals involves building a system of equations governing the material behavior under multi-axial stress states. In general, these equations require a hardening law that describes the stress-strain relationship. This study provides a thorough examination of the existing phenomenological hardening laws in the literature. Based on their ordinary differential equations, special efforts were made to discuss the degree of flexibility of these hardening laws. Four new

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... nomenological hardening laws were proposed during the discussions to capture the stress-strain relationship of automotive sheet metals, such as aluminum alloy and steel sheets. Then, applications of 18 hardening laws for fitting the uniaxial tensile stress-strain data of 12 automotive sheet metals were thoroughly compared. The comparisons reveal that the proposed hardening laws capture well the experimental stress strain data of all examined materials. Compared to several combined hardening laws, the proposed functions have comparable flexibility but require fewer parameters.