Abstract

In this work, two methodologies for the analysis of unidirectional fiber reinforced composite materials are presented.

The first methodology used is a generalized anisotropic large strains elasto-plastic constitutive model for the analysis of multiphase materials. It is based on the mixing theory of basic substance. It is the manager of the several constitutive laws of the different compounds and it allows to consider the interaction between the compounds of the composite materials. In fiber reinforced composite materials, the constitutive behavior of the matrix is isotropic, whereas the fiber is considered orthotropic. So, one of the constitutive model used in the mixing theory needs to consider this characteristic. The non-linear anisotropic theory showed in this work is a generalization of the classic isotropic plasticity theory (A Continuum Constitutive Model to Simulate the Mechanical Behavior of Composite Materials, PhD Thesis, Universidad Politécnica de Cataluña, 2000). It is based in a one-to-one transformation of the stress and strain spaces by means of a four rank tensor.

The second methodology used is based on the homogenization theory. This theory divided the composite material problem into two scales: macroscopic and microscopic scale. In macroscopic level the composite material is assuming as a homogeneous material, whereas in microscopic level a unit volume called cell represents the composite (Tratamiento Numérico de Materiales Compuestos Mediante la teorı́a de Homogeneización, PhD Thesis, Universidad Politécnica, de Cataluña 2001). This formulation presents a new viewpoint of the homogenization theory in which can be found the equations that relate both scales. The solution is obtained using a coupled parallel code based on the finite elements method for each scale problem.

Abstract

International audience; Based on the finite element method, the wave finite element method (WFE) permits to analyze the dynamics of a periodic structure by using a wave decomposition of one period. This method reduces the number of DOF and it has advantages in calculation time. However, it cannot be applied easily to a railway track because this structure is subjected by moving loads which are not considered in a classical WFE. In this article, we present a technique to deal with moving loads applying in a railway track where the track components are modeled by 3D continuous media. By using the classical WFE for one track period in frequency domain, we can rewrite the vector of DOF and loads in a wave base. Then, we can calculate the wave amplitudes of the moving loads from their representation in this base. Thereafter, we apply the wave analyze of WFE to the hold structure. The result shows that the moving loads lead to a sum of wave amplitudes. Finally, we apply this method for a railway track subjected to constant moving loads with numerical application. The new technique permits to analyze the dynamic of railway tracks by considering only one track period.