A micropolar approach to microbuckling problems in unidirectionally reinforced polymer composites

Abstract

The present contribution considers the application of micropolar continuum theory to predict the microbuckling strength of microbuckling problems in long fiber reinforced composites and to extend simulations into the collapse regime. The approach considers a homogenized description at a coarse length scale where fiber and matrix phases are not individually resolved, but are represented indirectly via an effectively equivalent homogenized solid. The salient characteristic of this approach is its superior numerical efficiency over a fine-scale micromechanical representation where fibers and matrix would need to be discretized separately. A disadvantage of conventionally homogenized models, however, is the circumstance that fiber curvature is not accounted for. Hence, the local fiber bending stiffness cannot be preserved in the homogenization process and the strain localization stage of microbuckling problems is rendered ill-posed. Micropolar homogenization rectifies this deficiency by introducing additional rotational degrees of freedom to account for curvature strain. The present contribution distinguishes itself from earlier micropolar homogenization approaches by adapting a Total-Lagrangian finite strain plasticity theory for micropolar continua to the microbuckling problem under consideration here. From this theoretical basis, a constitutive model and a finite element formulation are derived, and the extra parameters introduced by the micropolar solid are identified.