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### Compression Molding of Discontinuous Fiber Composites, a Thermodynamics Approach to the Compaction Problem

#### Abstract

Discontinuous Fiber Composites (DFCs) constitute a new class of highperformance molding compounds that enable the use of compression molding as the manufacturing process of complex components with high volume fraction of fibers. However, the use of DFCs is still limited, one reason being the lack of theoretical modeling and numerical analysis methodologies enabling their use at full potential. During compression molding, the polymeric resin is brought above its melting temperature and thus the material system consists in the cohabitation of a fluid and solid component. In this paper we adopted a macroscopic point of view that consists in depicting the material system as an open thermodynamic system through which the fluid can flow thus yielding a macroscopically compressible system for which a specific state, referred to as the compaction point, exists. The compaction point denotes the state at which no relative motion of fluid can occur with respect to the solid one and thus the thermodynamics system becomes incompressible. A stabilized mixed finite element method is presented that allows for the direct solution of the compaction problem in which all variables are treated as primary ones. This method yields a generalized saddlepoint problem that is known to be stable only for specific coupling of interpolation orders between the primary variables. Circumventing the latter is achieved via a stabilization procedure based on the use of the Algebraic Sub-Grid Stabilization (ASGS) method that yields a fully stable Galerkin weak mixed formulation for equalorder interpolation between all primary fields. This method proves beneficial to highlight the physical phenomena occurring in compression molding of fiber-reinforced media.