A new mathematical framework called microstructure-sensitive design (MSD) has recently been developed to facilitate solutions to inverse problems in microstructure design, where the goal is to identify the complete set of relevant microstructures that are theoretically predicted to satisfy a set of designer-specified criteria on effective properties or performance. This methodology has been applied previously to a few design-related case studies, mainly involving polycrystalline metals. This article describes the first application of MSD methodology to customized design of continuous fiber-reinforced composites for specified combinations of performance criteria. The main contribution of this study is that it presents a novel but simple mathematical framework for the application of first-order MSD to the design problems involving continuous fiber-reinforced composites. In the examples presented in this article, elementary first-order theories spanning two length scales have been selected to obtain effective properties of continuous fiber-reinforced composite material systems. Having selected these first-order theories, the authors proceed to demonstrate the viability of applying the first-order MSD framework to design the case studies in continuous fiber-reinforced composites.
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