A Micropolar Phase Field Fracture Model for Elastoplastic Solids Applied to Concrete Failure

ABSTRACT Given the high costs and practical limitations of experimental testing, computational models have emerged as powerful alternatives to analyze and predict structural failures caused by fracture initiation and propagation. Many materials, such as concrete, rock, clay, certain ceramics, and various composites, exhibit quasi‐brittle or ductile cracking. Unlike brittle fractures, where the load capacity of the solid drops abruptly, the failure response of these materials is more involved and exhibits a gradual deterioration of structural integrity accompanied by plastic deformation. In these materials, depending on the loading conditions, fracturing begins with the formation of microcracks, which subsequently coalesce to form larger macroscopic ones. Additionally, under confined compression, localized zones of large inelastic deformations with dimensions linked to the material's microstructure can emerge. As a result, the fracture response of these materials is significantly influenced by their inherent microstructure, affecting both crack initiation and propagation. Therefore, a fracture model that explicitly accounts for the effects of microstructure on the macroscopic ductile fracture response of a body is essential. In this contribution, a thermodynamically consistent phase field fracture model for elastoplastic solids in micropolar continua is presented. We begin by reviewing the kinematical descriptions in which the effects of microstructure and microdeformation are incorporated through an independent microrotation field. Using a purely geometric approach, the evolution of fracture is linked to a constitutive crack driving functional. The governing equations alongside their finite element implementations are presented, and the constitutive relations for a solid with a general non‐associative plasticity formulation are detailed. A realization of the proposed framework specific to concrete is also introduced. We present a new degradation function alongside a crack driving force capturing the complex fracture response of concrete, including its pressure‐dependent strength and asymmetric response under tension and compression. Finally, the proposed framework is validated by comparing computational simulation results with existing experimental data across a range of loading conditions, from tension‐dominated to shear‐driven and compression‐induced failure scenarios. Comparison of load‐displacement curves and crack propagation paths with corresponding experimental observations demonstrates the capabilities of the proposed framework.