A Monolithic Finite Element Approach to Compute Permeabilityatc Microscopic Scales in LCM Processes

In this paper, a numerical approach for permeability determination at the mesoscopic and microscopic scales is proposed. In an eulerian framework, the computational domain (corresponding to the elementary cell) is composed of one single mesh, where the interface between the fibres (microscopic scale) or the yarns composing the fabric (mesoscopic scale) and fluid is captured through a level set approach. At the microscopic scale, Stokes equations are considered. At the mesoscopic scale, resolution of a coupled Stokes (in the fluid)Darcy (in the yarn) flow is necessary and is performed using also a mixed finite element technique, providing a single system of equations. Stabilization of the Brinkman flow is attained using the P1+/P1 element. Results on permeability computation at the microscopic scale, as well as sensitivity analysis, illustrate the methodology followed.