Data-driven modelling of the multiaxial yield behaviour of nanoporous metals

Nanoporous metals, built out of complex ligament networks, can be produced with an additional level of hierarchy. The resulting complexity of the structure makes modelling of the mechanical behaviour computationally expensive and time consuming. In addition, multiaxial stresses occur in the higher hierarchy ligaments. Therefore, knowledge of the multiaxial material behaviour, including the 6D yield surface, is required. Surrogate models, predicting the mechanical behaviour of the lower level of hierarchy, represented by finite element beam models, are a promising approach to overcome such challenges, when existing analytical models are not able to describe the material behaviour. Therefore, as a first step, we studied the elastic behaviour and the yield surfaces of representative volume elements with idealised diamond and Kelvin structure in finite element simulations. The yield surfaces showed pronounced anisotropy and could not be described by the Deshpande-Fleck model for isotropic solid foams. Instead, we used data-driven and hybrid artificial neural networks, as well as data-driven support vector machines and compared them regarding their potential for the prediction of yield surfaces. All considered methods were well suited and resulted in relative errors < 4.5 %. Support vector machines showed the best generalisation and accuracy in 6D stress space and are suitable for extrapolation outside the range of training data.