Multi-scale Modelling using Recurrent Neural Network for Mesoscale Surrogation to Achieve Acceleration in Simulation of Rate-Dependent Dissipative Lattice Based and Cellular Meta-Materials

FE2 complexity renders multi-scale cellular meta material simulations impractical on account of excessive time and (computational) resource requirements. Especially the rate dependent, dissipative material nature of the base material alongside the fine discretization of the underlying repeated lattices necessitates acceleration of the numerical scheme. Resolution of the micro scale boundary value problem by a surrogate is investigated and its applicability is demonstrated using lattice based meta materials.
An effective surrogate model sensitive to (strain) rate and (microscale) geometrical parameters using a recurrent neural network (RNN) is trained (offline) on a dataset populated by performing full-field simulations. Populating the dataset, including identification of generation parameters, establishing bounds for spanning a functional space, and designing of the surrogate model and tuning of the training parameters is presented.
The quality of the trained surrogate is evaluated by means of testing data and FE2 counterparts by substitution in equivalent multiscale simulations. Comparisons are made on the predictions demonstrating the sensitivity on (strain) rate, local constitutive behaviour, local (lattice) geometrical parameters using various loading scenarios.
One potential area of application for surrogated multiscale modelling is microscale level optimization to maximize / minimize an objective function defined on macroscale level. This is achieved by the reduction in computational resources enabling fast and cheap evaluation of the objective function (multiscale FE simulation).