Open Access

ARTICLE

On Multiscale Modeling Using the Generalized Method of Cells: Preserving Energy Dissipation across Disparate Length Scales

E. J. Pineda¹, B. A. Bednarcyk¹, A. M. Waas², S. M. Arnold¹

1 NASA GRC, Cleveland, OH, USA.
2 Felix Pawlowski Collegiate Professor, University of Michigan, Ann Arbor, MI, USA, and visiting Professor, Department of Aeronautics, Imperial College, London SW7, UK. Author for correspon-dence.

Computers, Materials & Continua 2013, 35(2), 119-154. https://doi.org/10.3970/cmc.2013.035.119

Abstract

A mesh objective crack band model was implemented within the generalized method of cells micromechanics theory. This model was linked to a macroscale finite element model to predict post-peak strain softening in composite materials. Although a mesh objective theory was implemented at the microscale, it does not preclude pathological mesh dependence at the macroscale. To ensure mesh objectivity at both scales, the energy density and the energy release rate must be preserved identically across the two scales. This requires a consistent characteristic length or localization limiter. The effects of scaling (or not scaling) the dimensions of the microscale repeating unit cell (RUC), according to the macroscale element size, in a multiscale analysis was investigated using a finite-notched, modified, double cantilever beam specimen. Additionally, the ramifications of the macroscale element shape, compared to the RUC, was studied.

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