Explicit double-phase-field formulation and implementation for bending behavior of UHPC-NC composite beams

Abstract

The Phase-field model emerges as a promising method since it can automatically capture the initiation, propagation, coalescence, and branching of cracks without any tracking algorithms. Despite its success in simulating brittle and quasi-brittle cracks, tensile (mode I) and shear (mode II) fractures cannot be distinguished effectively. Moreover, the phase-field model is rarely applied to specimens at the structural level (i.e., reinforced concrete beams), due to the demanding computational cost. To address these shortfalls, two sets of phase-field variables are formulated to describe the tensile and shear fractures of concrete, respectively, through crack-direction-based decomposition of strain energy density into tensile, shear and compressive parts. Computational burdens are greatly alleviated by implementing the model with an explicit finite element solver (Abaqus/Explicit), allowing for massive parallel computing. The sensitivity analysis is performed to investigate the effects of critical parameters with a 1D numerical tensile bar. The double-phase-field model is applied to study the bending behavior of composite beams consisting of normal-strength concrete (NC) overlayer and ultra-high performance concrete (UHPC) substrate. To this end, five UHPC-NC beams, with various thickness ratios of UHPC and NC layers, were prepared and loaded to failure. District bending strengths, cracking patterns, deformation characteristics and failure modes of the four beams were revealed and discussed. It shows that the proposed model is necessary to accurately capture the bending behavior of UHPC-NC composite beams. This model is also applied to discuss the effects of critical parameters on the bending behaviors of UHPC-NC composite beams. To benefit potential users, detailed explanations regarding the data structures of input files and user subroutines (VUEL, VUMAT, VUSDFLD in Abaqus/Explicit) are given and released on GitHub repository.