NUMERICAL SIMULATION OF HOMOGENIZATION OF 2D AND 3D COMPOSITE MATERIALS AND STRUCTURES USING THE UNIT CELL APPROACH

H. BADILLO; S. OLLER

Conferencia; V International Conference on Science and Technology of Composite Materials - COMATCOMP 09; 2009

This methodology proposes to find reliable estimates of the properties of the composite, to obtain the overall response of the structure, independently of the geometrical arrangement and of the material properties of the constituents using a homogenization technique based on a periodic microfield approach by studying a unit cell which represents the composite to be analyzed.The methodology is implemented based on a two-scale finite element code, a macroscopic and a microscopic scale. The macro scale treats the composite as a homogeneous material with anisotropic properties and deals with the boundary conditions and the loads applied in the model. The micro scale deals with the geometrical and the material properties of the constituents of the composite to obtain the homogenized response of the composite.The homogenized constitutive tensor of the composite is obtained thru perturbations of the unit cell for each Gauss point of the macroscale that enters in the nonlinear range and for each load increment. Periodic boundary conditions, by means of the Lagrange multipliers, are applied to ensure compatibility of deformations from one scale to the other.The homogenization technique is developed to obtain the response of 2D and 3D models for composite materials and composite structures with constituents that have classic constitutive equations, such as damage, plasticity, viscoelasticity, viscoplasticity, etc.In this paper the method is applied to analyze the structural response of a 3D model in the form of a simple supported reinforced concrete beam to demonstrate the applicability and consistency of this method.