Strain localization analysis in material nonlinear models

This paper presents a strain localization analysis in nonlinear models detached from constitutive models. The proposed implementation was performed on the INteractive Structural ANalysis Environment (INSANE) platform, an open source project developed by the Structural Engineering Department of the Federal University of Minas Gerais. Strain localization is associated with weak discontinuities and materials instabilities that occur during physically nonlinear structural analysis. Singularity of the acoustic tensor is considered the classical condition for strain localization and it can be calculated regardless of constitutive model selection. Localization analysis consists in searching for a unit vector which defines the direction at which the acoustic tensor becomes singular. This unit vector points towards the normal direction of the discontinuity surface in the body, which is created by the localization phenomenon. Localization analysis can be approached as a minimization problem of the acoustic tensor determinant. With parametrization techniques, it is possible to obtain the unit vector associated with the singularity. Strain localization analysis should be performed in each integration point (Gauss point), at each step of an incremental nonlinear analysis. At the end of localization analysis, one expects to detect points of material instabilities and use them as references for multiscale structural analysis.