  For multilayer structures, interfacial failure is one of the most important
elements related to device reliability. For cohesive zone modelling,
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 fit 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, three conditions are examined and implemented here: (i)
thermodynamic consistency, (ii) maximum energy dissipation path control and
(iii) J-integral conservation. 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. 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. The proposed
approach heralds a new autonomous, point-to-point constitutive modeling concept
for interface mechanics.

Computational Engineering, Finance, and Science