Análise de localização de deformações em modelos fisicamente não lineares

Abstract

This master's thesis presents a numerical technique for strain localization analysis in nonlinear material models. The proposed implementation was performed on the INSANE (INteractive Structural ANalysis Environment) platform, an open source project developed in the Structural Engineering Department of the Federal University of Minas Gerais. Material degradation usually occurs in a small and weaker portion of the body. This concentration of irreversible phenomena in a narrow material zone is commonly referred as strain localization. Numerically, strain localization is associated with the loss of ellipticity of differential equations governing the Boundary Value Problem. Considering the singularity of the acoustic tensor as general condition for localization, strain localization analysis consists in finding the direction at which the acoustic tensor becomes singular. Cartesian parametrization was used in this work, since it provides stability in the numerical solution process by relaxing the condition of the normal direction vector be of unit length. The implemented numerical technique was validated with simulations of increasing complexity. First, models with a predetermined localization zone were considered. Then, examples with experimental correspondence were simulated. Lastly, a comparison between the results of the implemented numerical technique and others methodologies was described.