An object-oriented framework for FE² multiscale analysis

Resumo

Computational Homogenization (CH) is a technique used to characterize the macroscopic material behavior using a computational RVE (representative volume element). It contrasts with the Analytical Homogenization (AH) strategies, where closed-form mathematical expressions are used (e.g. Rule of Mixtures and Mori-Tanaka). In offline CH approaches, the RVE is used to evaluate the material parameters required by the adopted constitutive lawof the macroscale model. Moreover, CH can also be performed on the fly (or online), as a mechanical analysis is performed at the macro-scale. In this case, no prior assumptions with respect to the material behavior at the lower level are required, allowing for modeling of complex microscale phenomena that would be difficult or impossible to capture with macroscopic constitutive models homogenized in an offline scheme. The so-called FE2 multiscale approach uses finite element models for both micro and macro scales. This work presents the computational implementation of a CH approach based on FE² into an academic finite element code developed in C++ using Object-Oriented Programming concepts. In the adopted approach, the micro-scale is related to integration points of the macro-scale model and the scale transition is carried out using appropriate averaging theorems and periodic boundary conditions. The software architecture adopted suitable design patterns for FE2 implementation, which is described using UML diagrams. The computational implementation is validated considering the analysis of mechanical components of particulate composites with metallic matrix and ceramic inclusions. The obtained results are compared with results available in the literature.