Modeling and characterization of complex composite structures is challenging due to uncertainties inherent in these materials. Uncertainty is present at each length scale in composites and must be quantified in order to accurately model the mechanical response and damage progression of this material. The ability to pass information between length scales permits multiscale models to transport uncertainties from one scale to the next. Limitations in the physics and errors in numerical methods pose additional challenges for composite models. By replacing deterministic inputs with random inputs, stochastic methods can be implemented within these multiscale models making them more robust.

This work focuses on understanding the sensitivity of multiscale models and damage progression variations to stochastic input parameters as well as quantifying these uncertainties within a modeling framework. A multiscale, sectional model is used due to its efficiency and capacity to incorporate stochastic methods with little difficulty. The sectional micromechanics in this model are similar to that of the Generalized Method of Cells with the difference being the discretization techniques of the unit cell and the continuity conditions. A Latin Hypercube sampling technique is used due to its reported computational savings over other methods such as a fully random Monte Carlo simulation. Specifically in the sectional model, the Latin Hypercube sampling method provides an approximate 35 % reduction in computations compared to the fully random Monte Carlo method. The Latin Hypercube sampling is a stratified technique which discretizes the distribution function and randomizes the input parameters within those discretized fields. Within this multiscale modeling framework, a progressive failure theory is implemented using these stochastic methods and a modified Hashin failure theory. With a combined stochastic method and progressive failure theory, this multiscale model is capable of modeling the uncertainty and material property variations for composite materials.

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