Multiscale modeling of viscoelastic shell structures with artificial neural networks

Abstract For acquiring the effective response of structures with complex underlying microscopic properties, numerical homogenization schemes have widely been studied in the past decades. In this paper, an artificial neural network (ANN) is trained on effective viscoelastic strain–stress data, which is numerically acquired from a consistent homogenization scheme for shell representative volume elements (RVE). The ANN serves as a feasible surrogate model to overcome the bottleneck of the computationally expensive calculation of the coupled multiscale problem. We show that an ANN can be trained solely on uniaxial strain–stress data gathered from creep and relaxation tests, as well as cyclic loading scenarios on an RVE. Furthermore, the amount of data is reduced by including derivative information into the ANN training process, formally known as Sobolev training. Studies at the material point level reveal, that the ANN material model is capable of approximating arbitrary multiaxial stress–strain states, as well as unknown loading paths. Lastly, the material model is implemented into a finite element program, where the potential of the approach in comparison with multiscale and full-scale 3D solutions is analyzed within challenging numerical examples.