  Computational multiscale methods for analyzing and deriving constitutive
responses have been used as a tool in engineering problems because of their
ability to combine information at different length scales. However, their
application in a nonlinear framework can be limited by high computational
costs, numerical difficulties, and/or inaccuracies. In this paper, a hybrid
methodology is presented which combines classical constitutive laws
(model-based), a data-driven correction component, and computational multiscale
approaches. A model-based material representation is locally improved with data
from lower scales obtained by means of a nonlinear numerical homogenization
procedure leading to a model-data-driven approach. Therefore, macroscale
simulations explicitly incorporate the true microscale response, maintaining
the same level of accuracy that would be obtained with online micro-macro
simulations but with a computational cost comparable to classical model-driven
approaches. In the proposed approach, both model and data play a fundamental
role allowing for the synergistic integration between a physics-based response
and a machine learning black-box. Numerical applications are implemented in two
dimensions for different tests investigating both material and structural
responses in large deformation.
