A new methodology for anisotropic yield surface description using model order reduction techniques and invariant neural network

Abstract

In this paper, we present a general methodology that we call spectral neural network (SNN) which enables to generate automatically knowing a few datapoints (eight at most), a sound and plausible yield surface for any variations of a given anisotropic material, e.g. batches of the same material or same type of material produced by a different supplier. It relies on the use of a reliable parametrization of a performant analytic orthotropic yield function for the generation of a large database of yield surface shapes and the singular value decomposition method to create a reduced basis. For a specific material, a surrogate model for the reduced basis coordinates is further constructed using few additional datapoints. The dense neural network is built such as to ensure that the invariance requirements dictated by the material symmetry as well as the convexity of the yield surface are automatically enforced. The capabilities of this new methodology are demonstrated for hexagonal closed packed materials titanium materials, which are known to be particularly challenging to model due to their anisotropy and tension–compression asymmetry. Furthermore, we show that the SNN methodology can be extended such as to include variations of multiple materials of vastly different plastic behavior and yield surface shapes. The in-depth analysis presented reveals the benefits and limits of the hybrid data-driven models for description of anisotropic plasticity.