Interphase Model and Phase-Field Approach for Strain Localization

Abstract

Quasi-brittle materials subjected to a high level of mechanical solicitations see the development in relatively narrow zone of micro-cracks that coalesce into stress free cracks. In this work, the problem of strain localization in elastoplastic materials exhibiting softening has been approached by applying the interphase model together with the phase-field theory. In particular, the narrow zone where strains concentrate, usually named process zone or localization band, is kinematically modeled using the interphase model, while the phase-field variable is introduced to regularize the contact strains at the interface between the plastic strain band and the surrounding material. This corresponds to diffuse the interphase in the volume of the solid body. The formulation of the problem has been developed in a classical way using the principles of thermodynamics. A key point consists in a Reuss/Sachs type homogenization of the inelastic contact strains through a weak Dirac delta function which takes the shape of the Mumford-Shah functional. The introduction of this kinematical hypothesis consistently leads to the complete set of the governing equations for a localized body. The model has been tested by means of analytical applications. The results show that the introduced strain regularization does not affect substantially the structural behavior, also the model can be easily used to replicate experimental results. The application of the proposed model may involve different contexts as the strain localization in soil mechanics, plastic hinge formation in reinforced concrete frames and delamination in composite materials. It should be noted that the calibration of model parameters for the comparison between numerical end experimental results can be performed easily, since no additional mechanical parameters are needed with respect to those that characterize the elastoplastic behavior.