PSI - Issue 42

Monika Středulová et al. / Procedia Structural Integrity 42 (2022) 1537– 1544 M. Strˇedulova´ et al. / Structural Integrity Procedia 00 (2019) 000–000

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ening occurs. Full account of the committees work may be found in Ref. (Van Mier et al., 1997), part of the results have also been published by Van Vliet and Van Mier (1996). Results of the experiments clearly show dependence of the specimen apparent compressive strength on the slenderness ratio when nontreated, high friction boundary con ditions are used. Given that low friction testing did not show similar tendencies, the di ff erences of the first case were confirmed to be attributed solely to the e ff ect of friction. Authors expand on the theory of zones described by Kotsovos (1983). They show the confined compression zones as having a conical shape. By lowering the slenderness ratio of the specimen, the triaxial compression zone is not reduced but rather takes larger portion of the specimens volume (see Figure 1, right-hand side), resulting in higher apparent strength of the specimen. Given the di ff ering stress states which occur, the failure mode changed in the experiments accordingly (Van Mier et al., 1997). For high slenderness specimens (or using low friction interface during experiments), microcracks may develop along the confined compression zones (Van Mier, 1984) and the specimen fails by tensile stress in the middle section, pronounced by splitting cracks, showing the well-known characteristic hour-glass failure (showed in Fig. 1, center-left). When the confined compression zones occupy most of the specimen (low slenderness ratio specimens with high friction coe ffi cient interface), the cracking tends to be less localized and occurs on the outer layer of the specimen instead. The above described works presumably led to the formulation of not only European codes as we use them today (Neville, 2012) to evaluate the strength of cylinders. The present paper aims to analyze the behavior with the help of a mesoscale discrete model. Series of experiments was performed on concrete cylinders of various slenderness ratios, using a steel, non-coated platen, creating an envi ronment with induced friction. The experiments were subsequently modeled, using multiple friction scenarios from friction free conditions up to fully restrained lateral movements. The results were compared to the experimental results on the bases of maximal force reached in the experiment or simulation. The complex mechanical behavior of concrete originates in its heterogeneous structure. According to Bolander et al. (2021), mesoscale structure of the material at the level of individual aggregates strongly a ff ects overall macro scopic behavior, because it translates to the formation of microcracks and fracture process zone, inherent to quasi brittle materials. The heterogeneity becomes crucial in the uniaxial compression situation, because it creates stress fluctuations in the perpendicular directions which lead to development of tensile splitting cracks. These fluctuations are zero on average and therefore no transverse stress (and therefore no splitting cracks) is observed in the homoge neous models. Hence, it is advantageous to model the material behavior under uniaxial compression at the mesoscale, i.e., to explicitly account for individual particles, pores and matrix between them. Several continuous mesoscale models of concrete mechanical behavior have been developed (Thilakarathna et al., 2020; Idiart et al., 2011). The continuity of the displacement field makes simulations of cracking somehow di ffi cult. Also the computational requirements of such model becomes very restrictive. Several advantages can be gain by using reduced kinematics by employing discrete model types. The computational cost is reduced and also cracking becomes easy to represent. The cracks between individual discrete units are oriented. Bolander et al. (2021) documents the potential of discrete mesoscale modeling in fracture simulations. Among di ff erent discrete mesoscale models, the Lattice Discrete Particle Model (LDPM) (Cusatis and Cedolin, 2007; Cusatis et al., 2011b,a) is arguably the most valued. It has been extended for various concrete types (Fascetti et al.; Bhaduri et al., 2021) and loading scenarios (Alnaggar et al., 2013; Smith and Cusatis, 2017). The present con tribution uses similar type of model implemented in an in-house software (Elia´sˇ et al., 2015; Elia´sˇ and Voˇrechovsky´ , 2020; Elia´sˇ and Cusatis, 2022). It considers a continuous domain where spherical aggregates are randomly placed. Dimensions of the spheres are given by a characteristic dimension of a chosen aggregate fraction and optimal packing distribution. Then, Laguerre tessellation is performed to obtain polyhedral rigid bodies representing the aggregates and surrounding matrix. Constitutive equation has vectorial form and it is applied at the planar contact between these bodies. Is is taken from Ref. (Cusatis and Cedolin, 2007) and simplified, the confinement e ff ects are omitted and damage treatment is modified. Cracking of the material translates to the model in the form of a single damage parameter D , which is obtained based on e ff ective strain e e ff and e ff ective stress s e ff . Ref. (Elia´sˇ, 2016) provides details regarding the constitutive formulation. 2. Mesoscale discrete model