On the computational analysis of microbuckling via mesoscale approaches

Abstract

The present treatise is concerned with the application of numerical models to the prediction of compressive strength and associated phenomena in fiber reinforced polymer matrix composites. This topic has received much attention by the scientific community, and the basic mechanisms at microscopic scale are well understood. Even so, microscale models and theories offer no predictive capability at scales relevant for practical application, and the problem of devising suitable approaches for this purpose is still wide open. The main obstacle in this endeavor is that relevant mechanisms are spread over several length scales, hindering their integration.

To address this challenge, the topic is thoroughly reviewed and mesoscale approaches are identified as an essential stepping stone towards an eventual transfer of fundamental scientific research to engineering application. Subsequently, the mesoscopic approach based on a homogenized representation of the fiber/matrix composite is developed further and its application for the prediction of the aforementioned mechanisms is demonstrated: Random flaws in local fiber alignment are the main source of uncertainty with regard to compressive strength and introduce a dependence of compressive strength on domain size. Methods for the proper representation of these flaws and their effect on compressive strength are considered and extended. Compressive failure in the materials under consideration is caused by shear strain localization and features characteristic width and orientation. To make these phenomena amenable to mesoscale modelling as a homogenized solid, the application of an extended solid theory with additional rotational degrees of freedom is considered. The versatility of the approach is demonstrated by predicting phenomena ranging from very small sizes, i.e. the bandwidth, to large sizes via the predicted scale law for compressive strength. Hence, it is argued that the mesoscale approach provides an excellent platform for further work concerned with component scale applications.