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Comparison of Multiscale and Kernel-based Correlations for Stochastic Permeability Models in Composites Manufacturing



Computational models simulating liquid injection processes for composites manufacturing typically invoke a porous medium representation of the fabric reinforcement material. This representation is an abstraction of the real medium in which flowing, reacting, and cooling resin interacts with meandering fibers. Stochastic permeability models have traditionally been introduced in an effort to capture the effect of this heterogeneity as it varies over the specimens. The choice of a probabilistic model for this random permeability field has strong implications on the statistical predictions relevant to cycle time, cost, and quality control. A standard approach to construct such a model is to assume it has a spatially invariant probability density function that is often described by a log-normal distribution. A spatial correlation function is then appended to the probabilistic structure by optimizing a covariance kernel over some predefined model class. This optimization approach is typically limited to the porous medium abstraction and thus completely ignores subscale features that pertain to the mechanical and geometric properties of fibers, lay-up, and forming operations. We first obtain a multiscale mechanistic solution for the forming process that characterizes the fiber shearing angles in terms of all of the subscale properties. We then invoke constitutive relations to map these shearing angles onto the local principal components of the permeability tensor. By using a polynomial chaos methodology, we obtain an explicit stochastic expression between the subscale properties and the spatially varying permeability field. The resulting permeability field is non-stationary and is strongly influenced by boundary conditions, geometry, and fiber properties. Its marginal distribution functions also exhibit significant spatial fluctuations. We construe this stochastic permeability field as being a good representation of reality, and using it, we then seek optimal representations against several classes of kernel-based covariance models.


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