The usage of fiber reinforced polymers (FRP) continues to increase due to their excellent specific properties and inherent lightweight potential. More recent developments focus on the application of FRP to laminates of increased thickness, further leveraging their benefits and opening up new areas of appliaction [1]. This inevetibly leads to more complex stress states in the laminates as opposed to the typically assumed plane stress conditions in thin laminates. Such generalized stress states pose a significant challenge to predicting the material’s behavior, especially when it comes to failure.
The fundamental problem of complex stress states posing a major challenge to established failure theories was thoroughly investigated in the second world wide failure excercise (WWFE-II) [2]. The results sparked the development of further, more advanced models trying to close the identified gap. Daniel Camanho et al. continued with the concept of an invariant based theory and validated it experimentally for superimposed hydrostatic pressure [3]. Daniel incorporated micromechanical concepts into a macroscopic theory, allowing for pre-failure yielding of the laminate [4]. With increasing computational ressources, explicit modeling of the microscale became more prominent. Sun et al. made extensive use of simulations based on representative volume elements (RVE) to generate data which they used to refine the NU-Daniel criterion [5]. Chen et al. take this one step further and rely solely on data obtained from RVE simulations to train a machine learning (ML) model to assess stress states of up to three superimposed stress components simultaneously [6]. Wan et al. follow a similar approach of training an ML model based on the results of RVE simulations [7]. They, however, deviate from the absoulute prediction of a single failure point, but rather leverage experimental data to assess failure probability of 2D failure envelopes.
Despite the significant research effort and notable results, none of the works address the fundamental challenge of simultaneous superposition of all six stress components. In recent work of ours, we showed that the assessment of such 6D stress states is in principal possible, leveraging simulations of a validated RVE to train a neural network (NN) as classifier [8]. In the proposed work, we extend the results to obtain material effort under arbitrary stress states via a deep NN. This significantly enhances the usability of the resulting failure assessment network (failNet), by imporving both accuracy as well as interpretebility of the results.
The improvements is traced back to the fact that, as opposed to typical classification tasks, an exact representation of the boarder between the different classes is of the utmost importance. The advancement from a previously binary decision where minimal increases in the stress state had to lead to a sudden change in predicted class, to a continuous rating of the stress state leads to a much more robust training. In addition to that, the proposed failNet’s prediction may be used to determine unexploited material capabilities and therefore potential to further reduce the material footprint of the structure at hand.
Approaches to ensure a representative generation of training for the failNet in the face of different failure modes will be elucidated. The capabilities of the proposed failNet will be compared to established failure theories both for classical 2D stress states as well as more complex superpositions.