Direct data-driven algorithms for multiscale mechanics

Computer Methods in Applied Mechanics and Engineering, vol. 433, pp. 117525

Abstract

We propose a randomized data-driven solver for multiscale mechanics problems which improves accuracy by escaping local minima and reducing dependency on metric parameters, while requiring minimal changes relative to non-randomized solvers. We additionally develop an adaptive data-generation scheme to enrich data sets in an effective manner. This enrichment is achieved by utilizing material tangent information and an error-weighted k-means clustering algorithm. The proposed algorithms are assessed by means of three-dimensional test cases with data from a representative volume element model.

Authors 4

1. Erik Prume corresponding Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, D-52074 Aachen, Germany

2. Christian Gierden

   Ruhr University Bochum

   Affiliation as printed

   Institute of Mechanics of Materials, Ruhr University Bochum, Universitätsstrasse 150, D-44801 Bochum, Germany

3. M. Ortíz

   California Institute of Technology · University of Bonn · Hausdorff Center for Mathematics

   Affiliation as printed

   Division of Engineering and Applied Science, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA

   Hausdorff Center for Mathematics, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

4. Stefanie Reese Aachen Institute of Applied Mechanics

   University of Siegen · RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Str. 1, D-52074 Aachen, Germany

   University of Siegen, Adolf-Reichwein-Str. 2a, D-57076 Siegen, Germany