Process-modeling of composites using two-phase porous media theory

A biphasic continuum model is proposed for the modeling of a family of forming processes for fiber composites. The processes considered involve deformation of a fiber bundle network, wetting by penetration of resin into fiber bundles, and resin flow through the fiber bundle network. The continuum model represents three (or more) actual micro constituents as two continuous phases: a solid phase being the fiber network plus any extra void within the fiber bundles and a fluid phase being the liquid matrix. The model framework thus comprises the continuum formulation of a nonlinear compressible porous solid saturated with an incompressible fluid phase. Guided by the entropy inequality, we specify constitutive relations concerning three different mechanisms pertinent to the forming process: effective stress response of the fiber bundle network, compaction of the solid phase, and Darcian interaction between the two phases. We are particularly concerned with the compaction of the fiber-bundles of the solid phase, consisting of elastic packing combined with a viscous wetting process driven by the fluid pressure. The paper is concluded with a couple of numerical examples, where the volumetric deformation-pressure response of a fluid saturated fiber bundle network at undrained conditions is considered. Both volumetric relaxation and volumetric creep tests are analyzed. In particular, the response for different loading rates is assessed. As a final example, a finite element analysis of a relaxation test for the macroscopically undrained compression of a fluid-filled fibernetwork specimen is carried out.