Quantitative Assessment of the Influence of Tensile Softening of Concrete in Beams under Bending by Numerical Simulations with XFEM and Cohesive Cracks

Abstract

Results of the numerical simulations of the size effect phenomenon for concrete in comparison with experimental data are presented. In-plane geometrically similar notched and unnotched beams under three-point bending are analyzed. EXtended Finite Element Method (XFEM) with a cohesive softening law is used. Comprehensive parametric study with the respect to the tensile strength and the initial fracture energy is performed. Sensitivity of the results with respect to the material parameters and the specimen geometry is investigated. Three different softening laws are examined. First, a bilinear softening definition is utilized. Then, an exponential curve is taken. Finally, a rational Bezier curve is tested. An ambiguity in choosing material parameters and softening curve definitions is discussed. Numerical results are compared with experimental outcomes recently reported in the literature. Two error measures are defined and used to quantitatively assess calculated maximum forces (nominal strengths) in comparison with experimental values as a primary criterion. In addition, the force—displacement curves are also analyzed. It is shown that all softening curves produce results consistent with the experimental data. Moreover, with different softening laws assumed, different initial fracture energies should be taken to obtain proper results.

Keywords

• concrete
• size effect
• fracture energy
• cohesive crack
• XFEM
• three-point bending