A micromorphic filter for determining stress and deformation measures from direct numerical simulations of lower length scale behavior

Abstract

AbstractA micromorphic filter is presented for the extraction of stress and deformation measures from underlying direct numerical simulation (DNS) of microstructural mechanical response. The filter is consistent with the micromorphic continuum theory of Eringen and Suhubi (1964), and allows the interrogation of a DNS to generate higher order constitutive models. The filter adopts aspects of the overlap coupling techniques for atomistic‐continuum scale‐bridging in order to update the nodal degrees of freedom of the finite‐element‐based filter. Two methods for the extraction of quantities of interest from the underlying DNS are presented. The first is a least squares fitting technique which is appropriate for finite‐element‐style macro‐scale domains, and the second is a variationally based approach which generalizes the method to any macro‐scale domain which has a variational form. No restrictions on the form of the micro‐scale simulation are inherent to the approach, provided that the required quantities (stress, position, etc.) can be provided. The filter is applied to a simple homogeneous medium undergoing homogeneous deformation to demonstrate the recovery of a classical continuum response, what we call the null case. We then apply the framework to the same homogeneous medium with a central and edge penny‐shaped crack to show micromorphic effects. We demonstrate that varying the size of the filter causes the micromorphic behaviors to arise and then dissipate as the filter becomes smaller than the crack's length scale. We also show the effect of filter size on a chiral element network along with a plate perforated with evenly spaced and perturbed holes through the thickness. The micromorphic effects are shown to be present for the chiral elements under any loading but become most pronounced when a single element is located within each averaging domain. Micromorphic effects become pronounced for the plate upon the onset of localization.