Modeling Material Fracturing with a Phase-Field Method Taking into Account Hydro-Mechanics Coupling and Material Heterogeneity

ABSTRACT We introduce a novel numerical approach for modeling cracking in heterogeneous materials by considering hydromechanical coupling. The proposed approach addresses the need for more accurate models to study cracking processes in materials with mineral heterogeneity, which are frequently encountered in geomechanics and civil engineering applications. A new phase field model is developed to describe the transition from diffuse damage to localized cracks, including both tensile and shear cracks. The model incorporates an elastic-plastic constitutive law to describe the basic mechanical behavior of the material. We account for mineral heterogeneity by considering the mineral compositions of rock-like materials, such as inclusion content, which affect the macroscopic elastic properties of the material. The proposed model is applied to analyze desiccation and mechanical tests performed on mortar. We compare the numerical results with experimental measurements to demonstrate the accuracy of the proposed model. INTRODUCTION Based on laboratory tests and in-situ monitoring, it has been observed that rock-like materials commonly experience failure as a result of the initiation and propagation of fractures and cracks. These materials are subjected not only to mechanical loading, but also to changes in water saturation, temperature, and chemical degradation. Hence, it is imperative to conduct an analysis of the damage mechanics of these materials by accounting for the multi-physical coupling phenomena. Over the past few decades, numerous phenomenological damage models have been proposed for various engineering materials, including rocks and concrete. Many of these models were developed within the framework of thermodynamics and employed a scalar internal variable for isotropic damage (Jefferson and Mihai, 2015; Chen et al., 2015; He et al., 2015) or tensorial variables for anisotropic damage (Voyiadjis et al., 2008; Desmorat, 2016; Zafati and Richard, 2019). In these models, the connection between macroscopic behavior and microscopic crack evolution is not explicitly established. More recently, the phase field method has emerged as a powerful tool for modeling the transition from diffuse damage to localized cracks (Bourdin et al., 2000; Miehe et al., 2010a,b; Borden et al., 2012; Ambati et al., 2014), by approximating sharp cracks with regularized smeared cracks. Various formulations have been proposed for modeling tensile, shear, and mixed cracks in elastic materials. Additionally, several phase-field models have incorporated the coupling between plastic deformation and damage evolution (Miehe et al., 2015a; Borden et al., 2016; Areias et al., 2016; Samaniego et al., 2021; Khalil et al., 2022).