Um estudo sobre estimativas de erro de modelagem em estruturas de materiais heterogêneos

Abstract

This work presents a study on modeling error estimates in linear elastic structures of heterogeneous materials. The employed formulation is based on a theory of a posteriori estimation of modeling errors and uses the Finite Element Method as numerical tool. The evaluated modeling errors consist of global errors based on energy norm and local errors in quantities of interest induced by replacing the fine-scale micromechanical properties of the material by homogenized or effective properties. These effective properties are determined from different micromechanical models and considered in the surrogate physical models of the heterogeneous materials. The quantities of interest may be, for example, averaged stress or strain on chosen regions, such as surfaces of inclusions, and interfacial displacements. Several numerical examples involving structures of heterogeneous materials are analyzed and the results are presented to demonstrate the performance of the formulation in the evaluation of global and local modeling errors.