A PCE-based multiscale framework for the characterization of uncertainties in complex systems

This paper presents a framework for the modeling and analysis of material systems that exhibit uncertainties in their constituents at all scales. The framework integrates multiscale formalism with a polynomial chaos construction enabling an explicit representation of quantities of interests, at any scale, in terms of any form of underlying uncertain parameters, a key feature to model multiscale dependencies. It is demonstrated how the framework can successfully tackle settings where a hierarchy of scales must be explicitly modeled. The application of this framework is illustrated in the construction of stochastic models of mesoscale and macroscale properties of non-crimp fabric composites. Joint statistical properties of upscaled components of the composite, including properties of tow, laminae and laminate, are computed.