Calibration of Micromorphic Constitutive Models from Variationally Filtered Direct Numeric Simulations

Granular and other heterogeneous materials exhibit complex behaviors which are difficult to capture using classical continuum theories. Enhancements through higher order descriptions of the deformation such as micropolar or, most generally, micromorphic continuum have been proposed but suffer from difficulty in calibrating the numerous parameters. We here propose and demonstrate a variationally based method for computing, or “filtering,” the deformation and stress response of a Direct Numeric Simulation (DNS) to the micromorphic macro-scale utilizing only the continuum equations of Eringen and Suhubi. Once determined for several DNS, we calibrate micromorphic finite deformation elastoplastic constitutive equations within the context of a surrogate-based Bayesian uncertainty quantification framework and comment on upcoming extensions.