Numerical technique for strain localization analysis considering a Cartesian parameterization

This paper presents a numerical technique for strain localization analysis in nonlinear material models considering a Cartesian parameterization. As a result of material’s natural heterogeneity, degradation often occurs in a small and weaker portion of the body. This concentration of irreversible phenomena is commonly referred as strain localization. From a kinematic standpoint, strain localization is associated with weak discontinuities that occur during physically nonlinear structural analysis. In a numerical simulation, it is linked with the loss of ellipticity of differential equations governing the boundary value problem. Singularity of the acoustic tensor is considered the classical condition for strain localization. It can be approached via analytical formulations or numerical techniques. Such a parameterization was utilized to define the normal direction to the discontinuity surface. Localization analysis was performed at material level after the convergence of each step in a set of nonlinear analyses. After the simulations, valuable information is available to regularization methods.