Do We Need Complex Constitutive Models to Simulate the Concrete Gap Test?

The gap test [1] is a recently introduced non-trivial experiment designed to evaluate the effect of crack-parallel stresses on the tensile strength and fracture energy of materials and to benchmark constitutive models for concrete, as suggested by its conceptual author, Z.P. Bažant. Although the setup resembles a three-point bending test of a notched beam, the defining difference is the initial preloading stage. In this stage, the central part of the specimen is vertically compressed, and this load is maintained during the subsequent bending phase. Experimental data indicate that low-magnitude preloading has a favorable effect on the bending response, whereas higher magnitudes lead to a significant reduction in strength. Preliminary results from our recent numerical study [2] suggested that structural effects present in the experiment may outweigh the impact of the constitutive model behavior under complex multiaxial stress states. Those simulations, performed in the OOFEM platform [3], employed the CDPM2 damage-plasticity model for concrete failure by Grassl and coworkers [4], calibrated on conventional three-point bending tests across three specimen sizes to ensure the size effect was captured correctly. This contribution compares the response obtained with the sophisticated CDPM2 model with that of a simple isotropic damage model featuring exponential softening and a smoothed Rankine expression for the equivalent strain. The responses are compared to the entire experimental dataset, consisting of three specimen sizes and three levels of preloading. Finally, we investigate whether modifying the dimensions of the preloading plates can diminish the parasitic structural effects observed in the original setup.

References

1. H. T. Nguyen, M. Pathirage, G. Cusatis, and Z. P. Bažant, Gap test of crack-parallel stress effect on quasibrittle fracture and its consequences, Journal of Applied Mechanics, 87(7):071012, 2020.
2. M. Jirásek and C. Li, Lessons learned from simulations of the gap test, Computational Modelling of Concrete and Concrete Structures, 2026, https://doi.org/10.1201/9781003660026-66.
3. B. Patzák and Z. Bittnar, Design of object oriented finite element code, Advances in Engineering Software, 32(10-11):759-767, 2001.
4. P. Grassl, D. Xenos, U. Nyström, R. Rempling, and K. Gylltoft, CDPM2: A damage-plasticity approach to modelling the failure of concrete, International Journal of Solids and Structures, 50(24):3805–3816, 2013, https://doi.org/10.1016/j.ijsolstr.2013.07.008.