Multi-Scale Failure Analysis of Laminated Composites Using the Boundary Element Method

Abstract

This project has as its main objective the development of the computational tools capable of facilitating multi-scale failure analysis in laminated composites. First, for the continuum meso-scale, the boundary element method (BEM) is used, in which the anisotropic 3D fundamental solutions based on double Fourier series were employed. The most significant advantage of using this Fourier series representation and its derivatives is that Fourier coefficients need to be evaluated just one time independent of the number of field points. This fact reduced the computational efforts, besides facilitating the ease of implementation into a BEM code. The dynamic effects in the continuum media were included in the equilibrium equation. These effects induced domain integrals in the boundary integral equation (BIE). The Dual Reciprocity Method (DRM) and the Radial Integration Method (RIM) were implemented for the transformation of the domain integrals into boundary integrals. Additionally, an acceleration technique namely the Adaptive Cross Approximation (ACA) was used with the BEM. The combination of the 3D anisotropic fundamental solutions with ACA resulted in a substantial memory and processing speed gain, that is of main importance when huge numerical problems, such as multi-scale problems, are being analized. Next, the failure multi-scale criterion was implemented and applied to laminated composites. For the micro-scale analysis, a specific potential for epoxy materials was used. Then, the Cauchy-Born rule was used to couple the scales on the 3D multi-scale model. Some numerical examples were presented in order to show the validity of the failure criterion. The project involved a one-year period at Carleton University in Ottawa, Canada, under the supervision of Prof. Dr. Choon-Lai Tan, specialist in fracture mechanics, anisotropic material formulation and boundary elements. This period in Canada provided the student with a strong academic formation, besides, providing the possibility of obtaining a double diploma. Through a cotutelle agreement, the student will receive a Ph.D. degree from Carleton University as well as from UNICAMP.