In this work, we present a multiscale model for architected lattices that captures material nonlinearities due to yield and plastic hardening, as well as geometric nonlinearities including buckling, post-buckling softening, and densification. We employ an FE^2 approach where the component-scale deformation is modeled by finite element (FE) analysis and the microscale deformation is modeled by another FE simulation of the representative unit cell (RUC). A homogenization scheme is used to determine the stress-strain constitutive relation for the component-scale FE simulation through numerous evaluations of the RUC. The model is integrated into a computational framework for multiscale modeling that handles resource management and fault tolerance to allow many RUC evaluations to occur in parallel, enabling efficient use of high-performance computing resources.
While the FE^2 approach provides significant computational savings over large-scale discrete simulations, the total computational cost is still immense due to the repeated evaluations of the lower-scale model at every time step and material point. Further efficiency of our multiscale method is achieved through the development of an on-the-fly surrogate model. The adaptive surrogate model eliminates repeated evaluations of the lower scale at points in the input space that are the same as, or sufficiently close to, points that have already been sampled, without the need for offline training. We employ Gaussian process regression to assess uncertainty in the surrogate model at each lower-scale evaluation, providing a quantitative metric for determining when to evaluate the lower-scale model and when to use the response predicted by the surrogate model.
