A Microstructure-based Graph Neural Network for Accelerating Multiscale
  Simulations
J. Storm I. B. C. M. Rocha F. P. van der Meer
Simulating the mechanical response of advanced materials can be done more
accurately using concurrent multiscale models than with single-scale
simulations. However, the computational costs stand in the way of the practical
application of this approach. The costs originate from microscale Finite
Element (FE) models that must be solved at every macroscopic integration point.
A plethora of surrogate modeling strategies attempt to alleviate this cost by
learning to predict macroscopic stresses from macroscopic strains, completely
replacing the microscale models. In this work, we introduce an alternative
surrogate modeling strategy that allows for keeping the multiscale nature of
the problem, allowing it to be used interchangeably with an FE solver for any
time step. Our surrogate provides all microscopic quantities, which are then
homogenized to obtain macroscopic quantities of interest. We achieve this for
an elasto-plastic material by predicting full-field microscopic strains using a
graph neural network (GNN) while retaining the microscopic constitutive
material model to obtain the stresses. This hybrid data-physics graph-based
approach avoids the high dimensionality originating from predicting full-field
responses while allowing non-locality to arise. By training the GNN on a
variety of meshes, it learns to generalize to unseen meshes, allowing a single
model to be used for a range of microstructures. The embedded microscopic
constitutive model in the GNN implicitly tracks history-dependent variables and
leads to improved accuracy. We demonstrate for several challenging scenarios
that the surrogate can predict complex macroscopic stress-strain paths. As the
computation time of our method scales favorably with the number of elements in
the microstructure compared to the FE method, our method can significantly
accelerate FE2 simulations.