Abstract
The present work aims at the identification of the effective constitutive behavior of 5
aluminum grain boundaries (GB) for proportional loading by using machine learning
(ML) techniques. The input for the ML approach is high accuracy data gathered in
challenging molecular dynamics (MD) simulations at the atomic scale for varying
temperatures and loading conditions. The effective traction-separation relation is
recorded during the MD simulations. The raw MD data then serves for the training of an
artificial neural network (ANN) as a surrogate model of the constitutive behavior at the
grain boundary. Despite the extremely fluctuating nature of the MD data and its
inhomogeneous distribution in the traction-separation space, the ANN surrogate
trained on the raw MD data shows a very good agreement in the average behavior
without any data-smoothing or pre-processing. Further, it is shown that the trained
traction-separation ANN captures important physical properties and is able to predict
traction values for given separations not contained in the training data. For example,
MD simulations show a transition in traction-separation behaviour from pure sliding
mode under shear load to combined GB sliding and decohesion with intermediate
hardening regime at mixed load directions. These changes in GB behaviour are fully
captured in the ANN predictions. Furthermore, by construction, the ANN surrogate is
differentiable for arbitrary separation and also temperature, such that a
thermo-mechanical tangent stiffness operator can always be evaluated. The trained
ANN can then serve for large-scale FE simulation as an alternative to direct MD-FE
coupling which is often infeasible in practical applications.
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