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

摘要

Computational models simulating liquid injection processes for composites manufacturingtypically invoke a porous medium representation of the fabric reinforcement material. Thisrepresentation is an abstraction of the real medium in which flowing, reacting, and cooling resininteracts with meandering fibers. Stochastic permeability models have traditionally beenintroduced 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 onthe statistical predictions relevant to cycle time, cost, and quality control. A standard approach toconstruct such a model is to assume it has a spatially invariant probability density function that isoften described by a log-normal distribution. A spatial correlation function is then appended to theprobabilistic structure by optimizing a covariance kernel over some predefined model class. Thisoptimization approach is typically limited to the porous medium abstraction and thus completelyignores 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 processthat characterizes the fiber shearing angles in terms of all of the subscale properties. We theninvoke constitutive relations to map these shearing angles onto the local principal components ofthe permeability tensor. By using a polynomial chaos methodology, we obtain an explicitstochastic expression between the subscale properties and the spatially varying permeability field.The resulting permeability field is non-stationary and is strongly influenced by boundaryconditions, geometry, and fiber properties. Its marginal distribution functions also exhibitsignificant spatial fluctuations. We construe this stochastic permeability field as being a goodrepresentation of reality, and using it, we then seek optimal representations against several classesof kernel-based covariance models.