Permanent strains and post-peak tensile response of concrete by three-phase conceptual modeling

Plain concrete exhibits pronounced stress softening and permanent strains in uniaxial cyclic tension. The permanent strains in concrete have been measured since the 1980s by repeated tensile loading–unloading sequences. Nevertheless, accurately modeling the permanent strains, as well as the post-peak response, is still a challenge. To overcome it, we propose a conceptual three-phase modeling of concrete discretized by finite elements, consisting of an elastic aggregate phase, a perfectly plastic Interfacial Transition Zone (ITZ), and an anisotropically damaging mortar phase. Damage in mortar is assumed to be anisotropic and governed by extensions. The corresponding anisotropic damage model is a nonlocal one. The positivity of the intrinsic dissipation is checked. Mesh independency is gained by nonlocal integral averaging of the Mazars equivalent strain acting in the damage criterion function. The permanent strain and post-peak response of Terrien (1980) and Gopalaratnam and Shah (1985) experimental tensile references are accurately reproduced. • Meso-scale of concrete by three-phase conceptual modeling. • Tensile permanent strain and post peak response of concrete. • Nonlocal anisotropic damage model for mortar/elastic aggregates/ perfect plastic ITZ. • The permanent strains and post-peak responses of Terrien (1980) and Gopalaratnam and Shah (1985) experimental tensile references are accurately reproduced.