Multi-Scale Modeling of the Stochastic Micro-Mechanical Response of Fibrous Composite Materials Based on Local Estimation and Control of Modeling Errors

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A multi-scale modeling methodology of the micro-mechanical response of fibrous composites is established. The proposed work considers nonlinear elastostatics problems in which there exists uncertainty in problem data such as material characteristics, boundary data, and loading conditions. The approach is based on the notion of model validation by controlling the modeling errors in terms of stochastic micro-scale features that are instrumental in the initiation and progression of micro-mechanical failure mechanisms. The research objectives are to: 1) investigate several variations of multi-scale modeling techniques in which easily computable homogenized material models are locally enhanced with the stochastic micro-structure; 2) develop estimates of the modeling errors, incurred by using the multi-scale surrogate descriptions; and 3) establish a methodology that can address two types of uncertainty in the problem: those governed by random variables with known probability distributions and those provided in terms of worst-case scenarios.The broader societal benefits of the proposed work are evident from the realization that heterogeneous media are encountered in many engineering disciplines such as: electrical engineering (heterogeneous conducting media), biomechanics and biomedical engineering (heterogeneities in soft tissue or bones), civil engineering (concrete structures), or petroleum engineering (subsurface flow through porous media). All those applications are inevitably accompanied with uncertainty in the problem data, generally obtained through experimental measurements (thus, inherently statistical in nature). Outreach initiatives on the high school, undergraduate, and graduate levels are proposed.