Data driven modeling of interfacial traction–separation relations using a thermodynamically consistent neural network

Abstract

For multilayer structures, interfacial failure is one of the most important elements related to device reliability. For cohesive zone modeling, traction–separation relations represent the adhesive interactions across interfaces. However, existing theoretical models do not currently capture traction–separation relations that have been extracted using direct methods, particularly under mixed-mode conditions. Given the complexity of the problem, models derived from the neural network approach are attractive. Although they can be trained to model data along the loading paths taken in a particular set of mixed-mode fracture experiments, they may fail to obey physical laws for paths not covered by the training data sets. In this paper, a thermodynamically consistent neural network (TCNN) approach is established to model the constitutive behavior of interfaces when faced with sparse training data sets. Accordingly, four conditions are examined and implemented here: (i), positive energy dissipation; (ii), maximum energy 10 dissipation; (iii), conservation of the J-integral; (iv), dependence of interfacial toughness on the fracture mode-mix. These conditions are treated as constraints and are implemented as such in the loss function. The feasibility of this approach is demonstrated by comparing the modeling results with a range of physical constraints and several different input data sets. Moreover, a Bayesian optimization algorithm is then adopted to optimize the weight factors associated with each of the constraints in order to overcome convergence issues that can arise when multiple constraints are present. The resultant numerical implementation of the ideas presented here produced well-behaved, mixed-mode traction–separation​ surfaces that maintained the fidelity of the experimental data that was provided as input. Some guidance is also provided on the desirable features of input data sets. The proposed approach heralds a new autonomous, point-to-point constitutive modeling concept for interface mechanics.