On Some Problems in Determining Tensile Parameters of Concrete Model from Size Effect Tests

Abstract

The paper presents results of numerical simulations of size effect phenomenon in concrete specimens. The behaviour of in-plane geometrically similar notched and unnotched beams under three-point bending is investigated. In total 18 beams are analysed. Concrete beams of four different sizes and five different notch to depth ratios are simulated. Two methods are applied to describe cracks. First, an elasto-plastic constitutive law with a Rankine criterion and an associated flow rule is defined. In order to obtain mesh independent results, an integral non-local theory is used as a regularisation method in the softening regime. Alternatively, cracks are described in a discrete way within Extended Finite Element Method (XFEM). Two softening relationships in the softening regime are studied: a bilinear and an exponential curve. Obtained numerical results are compared with experimental outcomes recently reported in literature. Calculated maximum forces (nominal strengths) are quantitatively verified against experimental values, but the force – displacement curves are also examined. It is shown that both approaches give results consistent with experiments. Moreover, both softening curves with different initial fracture energies can produce similar force-displacement curves.

Size effect analysis of quasi-brittle fracture with localizing gradient damage model

“…It is easily observed that both elastic and post-peak softening responses match well with the experimental data for all cases considered. This is a huge improvement compared to the conventional nonlocal enhancement, discussed comprehensively by Gr egoire et al ( 2013); Havla´sek et al (2016); Marzec and Bobi nski (2019a) in the context of integral approach, and is thus not repeated here. A brief presentation with the conventional gradient enhancement was presented by Wosatko et al (2018), and also demonstrated briefly in third section where the same set of parameters cannot be used for the notched and unnotched beams considered.…”

“…Since conventional nonlocal enhancements cannot describe the evolution and propagation of damage process zones correctly, they are inadequate in capturing both types of size effects. This limitation was reported extensively for the integral approach (Gr egoire et al, 2013;Havla´sek et al, 2016;Marzec and Bobi nski, 2019a), and briefly illustrated for the gradient approach in Wosatko et al (2018).…”

“…In this paper, we focus on the size effect phenomenon in the three-point bend test of concrete beams, which is characterized by the relative size between FPZ and beam depth. Depending on the FPZ characteristics, a Type 1 or 2 size effect is observed (Gr egoire et al, 2015;Marzec and Bobi nski, 2019a). Correspondingly, a numerical model has to capture the evolution and propagation of FPZ correctly, in order to predict the size effect accurately.…”

“…In the context of the conventional nonlocal integral enhancement, much work has been reported on its inadequacy for structural size effect predictions, i.e. the structural responses of geometrically similar concrete beams cannot be accurately reproduced with a single set of material parameters, for both elasticity-based isotropic damage models (Gr egoire et al, 2013;Havla´sek et al, 2016) and elasto-plasticity models (Marzec and Bobi nski, 2019a).…”

Formulation and experimental validation of space-fractional Timoshenko beam model with functionally graded materials effects

“…deformation of a material body -the crux of this paper) in relation to its dimensions, date to the investigations of Leonardo da Vinci at the very beginning of XVI century [1,2]. Since that time both experimental techniques [3][4][5][6][7] and theoretical concepts [8][9][10][11][12][13] for SE analysis were considerably developed and moreover SE phenomena were utilised successfully in the modern industry [14][15][16][17][18]. The main message is that from the standpoint of mechanics, which constitutes the central point of presented considerations, one can say that each structure, due to the complexity of material over different scales of observation, reveals SE.…”