For multilayer structures, interfacial failure can be one of the most important issues related to their reliability. The traction-separation relations associated with the adhesive interactions at the interfaces that are inherent to such structures often depend on the fracture mode-mix, or combination of tension and shear at the interface. However, current theoretical models are unable to capture the traction-separation relations that have been extracted by recent developments in the direct extraction of mixed-mode traction-separation relations. Although neural networks can follow such data along the loading paths prescribed in the experiments, they fail to obey physical laws for areas not covered by the training data sets, due to the lack of mechanics input in such approaches. 
In this paper, a thermodynamically consistent neural network (TCNN) is proposed to model the interfacial traction-separation relations obtained from sparse training data sets. Three physically consistent conditions are considered and implemented via neural networking: thermodynamic consistency, selecting the local fastest energy dissipation direction and maintaining a fixed ratio between normal and tangential tractions along proportional loading paths. By treating these physical consistent conditions as constraints and implementing them as loss function terms, the whole traction-separation surface is constrained in order to provide reasonable results. The feasibility of this approach is approved by comparing the modeling results with a different number of physical constraints. Moreover, the Bayesian optimization algorithm is adopted to optimize the hyper parameters of the TCNN network in order to overcome convergence issues when multiple constraints are in present.


Data Driven Modeling of Interfacial Traction Separation Relations using a Thermodynamically Consistent Neural Network

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