Multiphase Systems with Applications to Composite Materials Manufacturing

The present thesis is devoted to the mathematical modeling of an industrial process of production of composite materials, in the framework of the theory of porous media. The following Introduction is devoted to the presentation of the main process problems concerning the production of composite materials and the most important applications. The first part of the thesis is dedicated to an introduction to continuum mechanics. In the first three chapters the basic theory of a single component continuum is presented, introducing some geometrical and kinematics tools, the balance equations in both a three dimensional and a two dimensional continuum, and the constitutive theory, stressing the principle of thermal admissibility. The fourth chapter is dedicated to a general introduction to the theory of multiphase systems. The second part is focused on applications. The first chapter presents the main results of the theory of porous media which are used to build the models of composite materials discussed in the subsequent chapters. The second chapter is dedicated to the study of the inertial terms in a problem of infiltration of a resin in a reinforcement matrix during a pressure driven RTM process. As a consequence of the application of the pressure, the border in which the resin permeates starts to oscillate. A qualitative and quantitative study of the oscillations is given, proving that inertial terms influences the dynamics of the process only at the beginning and then their effects decay. Based on such an observation, the third chapter takes into account a system in which the inertia is completely neglected, focusing on the infiltration of a reactive resin into a solid preform. The mouldability diagram (which gives a window of applicability in the space of the process parameters) is presented and an analytic approximated expression for the infiltration velocity is given.