PSI - Issue 47
Caroline Bremm et al. / Procedia Structural Integrity 47 (2023) 261–267 Author name / Structural Integrity Procedia 00 (2019) 000 – 000
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1. Introduction Mechanical compression tests have been used to measure the compressive strength of the materials, that is, the compressive stress necessary to deform or bring them to rupture. These tests are widely used in the civil construction field, more precisely, in the axial compression strength analysis of the concrete, a quasi-brittle material, being a fundamental mechanical property in choosing the most appropriate concrete composition for a structure. However, many factors (such as slenderness, roughness and restrictions between specimen and machine surface) can affect the estimation of compressive strength, which can lead to an inadequate application of its use in design (Van Mier et al. (1997); Bezerra (2016)). In such a context, numerical methods have been employed to complement both the available experimental data on compressive strength and the factors that may influence such a value. The numerical methods most used to study the phenomenon are the Boundary Element Method (BEM), the Finite Element Method (FEM), and the Discrete Element Method (DEM). Numerical simulations by using these methods allow the analysis of a wide range of materials and their peculiarities, in addition to reducing laboratory time and costs (Xue et al. (2020)). A class of discrete elements that have shown interesting results in the failure simulation is those where elements represented by bars or beams represent the continuum. In those cases, failure occurs when a critical force or strain is reached in such elements, initiating the damage process. Such a capability is advantageous in comparison to BEM and FEM to represent quasi-brittle materials failure because discontinuities appear naturally when the structure is under loading (Rios (2002), Munjiza et al. (2019), Huang et al.( 2022)). In the present work, a version of DEM named the Lattice Discrete Element Method (LDEM), where the continuum is discretized as a 3D-array of nodes linked by uniaxial bar elements spatially arranged and with masses concentrated at the nodes, is employed to simulate concrete specimens subjected to compression in order to evaluate the influence of boundary conditions and specimen geometry. More precisely, two types of contact boundary conditions are considered, and three different slenderness (height/width ratio - h/b) levels are analyzed (that is, h/b = 0.5, 1.0 e 2.0) by considering a square cross-section. Moreover, for h/b = 2.0, a circular cross-section is also examined. Two models are considered: one by using the LDEM and the second one by using a hybrid model, where LDEs are combined with FEs. In the hybrid model, the concrete is modelled by LDEs, whereas the steel platens, used to compress the sample, are modeled with FEs. 2. Lattice Discrete Element Method (LDEM) The basic formulation of the Lattice Discrete Element Method (LDEM) used in the present work has been presented in many research papers as, for example, in the works by Iturrioz et al. (2013) and Kosteski et al. (2020). Thus, only a brief description of the method is presented below. The LDEM consists in the discretization of the continuum as a 3D-array of nodes linked by uniaxial elements (also named bars in the following) spatially arranged, and with masses concentrated at the nodes. These bars are organized in a cubic arrangement (Fig. 1a) that is cubic cells with nine nodes, as proposed by Nayfeh and Hefzy (1978). Each node has three degrees of freedom, corresponding to the nodal displacements in three orthogonal directions. The condition of each bar to break is taken into account through the bilinear law, show in Fig. 1b, where F is the bar axial force and ε is the axial strain. Such a law directly depends on three local parameters, that is: EA i , ε u and ε p . The bar specific stiffness, EA i , is function of both the Young's modulus, E , and the cross-section area of the bar, A i , where i is equal to n for normal bar and to d for diagonal bar. The ultimate strain, ε u , is the strain value for which the element loses its load bearing capacity (that is the bar breaks), whereas the critical strain, ε p , is the strain at the crack initiation, function of a characteristic length of the material, d eq . The area under the bilinear law (triangle OAB in Fig. 1b) is related to the energy density needed to fracture the area of influence of the bar. Once the energy density equals the energy release rate (a material property), the element fails and loses its load carrying capacity. Thus, this nonlinear constitutive model allows both to reproduce the material damage and the element failure when a critical force condition is reached. Under compression, the material behaves linearly.
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