A phase-field model for strain localization analysis in softening elastoplastic materials

The present paper deals with the localization of strains in those structures consisting of materials exhibit- ing plastic softening response. It is assumed that strain localization develops in a finite thickness band separated from the remaining part of the structure by weak discontinuity surfaces. In view of the small thickness of the band with respect to the dimensions of the structure, the interphase concept is used for the mechanical modeling of the localization phenomenon. We propose a formulation for the quasi- static modeling of strain localization based on a phase-field approach. In this sense, the localization band is smeared over the volume of the structure and a smooth transition between the fully broken and the sound material phases is introduced. The mechanical performance of the model is illustrated for the case of uniaxial tensile test, discussing the instability of the force-displacement response, and for the case of three-point bending test, comparing the analytical results with the experimental ones.