Incorporation of tension-compression asymmetry into plastic damage phase-field modeling of quasi brittle geomaterials

Both experiments and theoretical investigations have evidenced the existence of compressive-shear fracture mode in geomaterials like concrete, rocks and gypsum. Proper description and modeling of intricate fracturing pattern with consideration of strong tension-compression asymmetry in mechanical response remain an open issue in phase-field modeling and simulation. In this work, a new phase field model with plasticity-damage coupling is formulated in the framework of irreversible thermodynamics. Two essential features, tension-compression asymmetry in mechanical response as well as two distinct fracture modes, are taken into account by incorporating two scalar-valued damage variables into the classical modeling framework. By defining a specific free energy density function, the coupling between damage and plasticity is achieved by involving a phase field variable into the yield function. The proposed model is validated at two levels. In the homogeneous cases, the mechanical behaviors of typical geomaterials are investigated in the plane stress condition. Meanwhile, a stress-based crack onset criterion is utilized to capture the distinct failure behavior both in tension and in compression. In numerical simulations, a local numerical integration with implicit return mapping algorithm and plasticity-damage decoupling treatment are developed. Three numerical examples are performed to demonstrate respectively the mode I, mixed-mode and model II fracture in geomaterials. Comparisons between numerical simulations and experimental data make it possible to evaluate the predictive performance of the proposed bi-dissipative phase field damage model. In addition, the local stress analysis is carried out to explain a changing mode of fracture propagation and to demonstrate the existence of tensile-shear (hybrid) fracture mode.