A coupled electro-thermo-mechanical discontinuous Galerkin method applied on composite materials

Carbon fiber reinforced polymer composites have become increasingly important due to their unique properties which are appreciated in many practical applications such as low weight, low cost, low density, high mechanical characteristics. Moreover the range of their electrical conductivity can be controlled by the amount of carbon fibers. Carbon fiber reinforced polymer composites consist of at least two components, a polymer matrix (generally dielectric) and electrically conductive fillers. This combination results in multifunctional composites, both structural and conductive. The existence of the polymer matrix will avoid catastrophic failure due to fiber breaking, and the existence of the carbon fibers will enhance strength and stiffness on one hand, and will allow to a significant temperature gradient when electric current is applied on the other hand. The objective of this paper is to study the response of the carbon fiber reinforced polymer composites when an electric power is applied and to determine the effective properties. To this end governing equations describing electro-thermo-mechanical coupling in composite materials are developed and discretized using the Discontinuous Galerkin (DG) finite element method. DG methods have many advantages such as optimal convergence and local approximation properties in addition to their flexibility for mesh adaption and their straightforward use of high order polynomial approximations. A micromechanical model of unidirectional carbon fibers dispersed in a polymer matrix is formulated considering the interaction of electrical, thermal and mechanical fields It is then solved using the DG method to determine the time dependent response of the electro-thermo-mechanical coupling and quantify the variation of the fields.