Non-homogeneous granular micromechanic-based numerical simulations for ultra-high-performance fiber-reinforced concrete (UHP-FRC) in compression, tension and three-point bending tests

Ultra-High Performance Fiber-Reinforced Concrete (UHP-FRC), a construction material that has been introduced and refined over the past two decades, offers exceptional advantages that set it apart from traditional concrete. The mechanical response of UHP-FRC is often evaluated in the laboratory using tests that include compression, tensile, and three-point bending, in which non-homogeneous deformation fields develop, resulting in the localization of failure processes. Here, we utilize a second gradient continuum theory, applicable to UHP-FRC, developed within the granular micromechanic framework to model the deformation and failure behavior. The granular micromechanic framework accounts for the variability in grain-pair orientations within a continuum material point, integrating interactions across the orientational space to capture the evolving macroscale behavior of UHP-FRC. A key outcome of the model is the prediction of directional evolution in damage and plasticity, leading to emergent anisotropy in the material’s response. As a result, a comprehensive micromechanic framework is developed that can characterize the deformation behavior of UHP-FRC, providing a robust connection between microscale processes and macroscale performance. This method incorporates Piola’s ansatz to link granular micromechanics with the continuum scale and introduces objective kinematic descriptors to represent grain-to-grain relative displacements under finite deformations. Evolution equations for damage and plastic variables, derived using Karush–Kuhn–Tucker (KKT)-type conditions, govern the interactions at the grain level. The model’s applicability is demonstrated through numerical simulations and comparisons with experimental tests in terms of the force–displacement curves. A parametric analysis is also conducted to assess the influence of input parameters on the simulation results. The model replicates the superior tensile and residual strength, excellent crack control, and remarkable resistance to crack propagation that enhance durability and structural integrity of UHP-FRC. The theoretical insights and analysis capability offered by the described model can form a basis for exploiting the immense potential of UHP-FRC for innovative and resilient applications in structural engineering.