Title: Multiscale analysis in solids with unseparated scales: fine-scale recovery, error estimation, and coarse-scale adaptivity

Authors: Joseph E. Bishop; Judith A. Brown; Theron M. Rodgers

Addresses: Component Sciences and Mechanics Department, Engineering Sciences Center, Sandia National Laboratories, Albuquerque, NM 87185, USA ' Fluid and Reactive Processes Department, Engineering Sciences Center, Sandia National Laboratories, Albuquerque, NM 87185, USA ' Computational Materials and Data Science Department, Material Sciences Center, Sandia National Laboratories, Albuquerque, NM 87185, USA

Abstract: There are several engineering applications in which the assumptions of homogenisation and scale separation may be violated, in particular, for metallic structures constructed through additive manufacturing. Instead of resorting to direct numerical simulation of the macroscale system with an embedded fine scale, an alternative approach is to use an approximate macroscale constitutive model, but then estimate the model-form error using a posteriori error estimation techniques and subsequently adapt the macroscale model to reduce the error for a given boundary value problem and quantity of interest. We investigate this approach to multiscale analysis in solids with unseparated scales using the example of an additively manufactured metallic structure consisting of a polycrystalline microstructure that is neither periodic nor statistically homogeneous. As a first step to the general nonlinear case, we focus here on linear elasticity in which each grain within the polycrystal is linear elastic but anisotropic.

Keywords: error estimation; model-form error; model adaptivity; uncertainty quantification; additive manufacturing; polycrystal; multiscale.

DOI: 10.1504/IJTAMM.2021.120799

International Journal of Theoretical and Applied Multiscale Mechanics, 2021 Vol.3 No.4, pp.329 - 362

Received: 20 May 2021
Accepted: 03 Sep 2021
Published online: 08 Feb 2022 *