Damage Development Analysis in Composite Materials by the BEM

Abstract

Continuum mechanics hinges on the concept of a Representative Volume Element (RVE) playing the role of a mathematical point of a continuum field approximating the true material microstructure. The RVE is very clearly defined in two situations only: (i) unit cell in a periodic microstructure, and (ii) volume containing a very large (mathematically infinite) set of microscale elements (e.g. grains), possessing statistically homogeneous and ergodic properties. The RVE or unit cell approach currently gains more and more importance in the numerical determination of generalized material behavior of multiphase materials, which are of sufficient length to capture all the average details of the microstructure.

One important goal of the mechanics and physics of heterogeneous materials is to derive their effective properties from the knowledge of the constitutive laws and spatial distribution of their components. Homogenization methods have been designed for this purpose. The basic idea behind RVEs is that the elastic energy stored inside a unit cell is identical to the one stored inside the represented homogenized continuum.

This paper deals with a multiscale approach to model heterogeneous materials, and using failure criteria, Tsai-Hill and maximum deformation, to detect any failure of the matrix and fiber, respectively. In the macroscale (global scale), the Boundary Element Method (BEM) for anisotropic plane elasticity was used to evaluate strain and stress fields in the domain of the lamina. These fields represent the macroscopic tensor of the structure, which is used to evaluate the boundary conditions in the microscale (local scale). Computer implementation of BEM and multi-scale approaches, to perform defect analyzes on composite laminates; Discussion of the results obtained from the multi-scale analysis and the failure are compared with the results obtained by other analyzes.