On the Use of Neural Networks in the Modeling of Yield Surfaces

The classic constitutive model of metal plasticity employs the concept of yield surface to describe the strain-stress response of metals. Yield surfaces are constructed as level sets of yield functions, which in turn are assumed to be homogeneous, smooth and convex. These properties ensure the mathematical consistency of the constitutive model while also facilitating the calibration of the yield function. The significant progress in computing hardware and software of the last two decades has opened new possibilities for research into general-purpose yield functions that are capable of capturing with high accuracy the mechanical properties of sheet metal. Here we investigate the modeling capabilities of yield functions defined by homogeneous, smooth and convex neural networks (HSC-NN). We find that small-sized HSC-NNs are capable of reproducing a wide range of convex shapes. This type of network is then ideally suited to data-driven frameworks based on virtual testing or on interpolation of data from mechanical tests, being easy to deploy in finite element codes. HSC-NNs are particularly adept at fitting aggregations of plane stress and out-of-plane data to build yield surface models accounting for 3D-stress states. We use them here to bring new insights into a recent cup-drawing experiment with aluminum alloy AA6016-T4. Finite element simulations with both plane stress and 3D models show promising results. In particular, the overall simulation run times of the HSC-NNs employed here are found to be comparable with those of conventional yield functions.