The negative environmental impacts of transportation are driving the development of lightweight structural materials that enable vehicle mass reduction and consequently lower emissions of harmful gases. Magnesium alloy AZ31 is a promising material due to its low density; however, its practical application requires a precise understanding of the mechanical response under complex loading conditions. The aim of this research was to develop a numerical model capable of predicting the multiaxial stress–strain response of the AZ31 alloy under cyclic loading with variable amplitude. The study consisted of both experimental and numerical parts. In the experimental part, a new design of a shear specimen and an improved shear testing fixtures were developed, enabling reliable cyclic testing. The numerical part involved an enhancement of an existing constitutive model through the implementation of a stable stress tensor update algorithm and a simplified procedure for determining material parameters. The developed model was validated using both original experimental results and data from the literature, demonstrating good agreement under uniaxial, shear, and proportional multiaxial loading conditions. The proposed approach represents a significant step toward physically grounded modelling of the cyclic behaviour of hexagonal close-packed alloys such as AZ31.
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