A DOUBLE SCALE METHOD FOR SIMULATING OF PERIODIC COMPOSITE MATERIALS

F. ZALAMEA; J. MIQUEL CANET; S. OLLER

Congreso; European Congress on Computational Methods in Applied Sciences and Engineering. ECCOMAS 2000; 2000

In this paper we present a numerical method in two scales in which structures made up of composite materials are simulated. The proposed method lies within the context of the homogenization theory and assumes the periodicity of the internal structure of the material. The problem is divided into two scales of different orders of magnitude: a macroscopic scale in which the body of the composite material is simulated, whereas at microscopic scale the material is simulated by an elemental volume called a cell. In this work, the homogenized strain tensor is related to the transformation suffered by the periodicity vectors. The homogenized stress tensor coincides with the classical theory of averages, moreover, the local equilibrium equation on the macroscopic scale is obtained. In this way, the problem of composite materials is posed as a coupled two-scale problem in which the composite material?s constitutive equation becomes the solution of the boundary value problem in the cell domain. For an overall solution to the problem, we present an algorithm which couples both scales by means of the finite elements method. Due to characteristics of this problem, the implementation proposed permits the simultaneous solution of the cell problems. The method?s validity can be seen by solving various examples found in the bibliography on this subject.