Issue 41

A. Mardaliazad et alii, Frattura ed Integrità Strutturale, 41 (2017) 504-523; DOI: 10.3221/IGF-ESIS.41.62 508 Figure 4 : The load-displacement diagram of the flexural test. The shape of the load-mid span displacement, represented in Fig. 4, indicates a significant non-linear behaviour until the failure. The failure is denoted by a sudden drop of the loading level. A study by Meda et al. [32], investigated Pietra-Serena sandstone under a flexural test. They performed the tests on specimens with different shapes and considered a notch in the middle-span of the specimens to assure that the crack takes place at the center. The experimental data provided by Meda et al. are in a good agreement with the results obtained during this research work where the geometries are similar to each other; i.e. the flexural strength and the load-displacement diagrams of the Meda’s work were reported as 9.1 MPa and 3.4 mm, respectively. N UMERICAL MODELLING any numerical modelling techniques have been developed for stress analyses of solid mechanics in the continuum domain. Among these, the non-linear Lagrangian Finite Element Method has its own privileges for a number of reasons, i.e. the accuracy and the convenient time consumption cost. However, a disadvantage lies within the reduced performance of grid-based numerical methods to deal with highly distorted elements and fragmentation. At present, the Smooth Particle Hydrodynamics (SPH) is one of the most convenient numerical methods to cope with problems related to large deformations and fracture. This method is a numerical mesh-free approach that represents the state of a system by a set of particles that hold the properties of the material. The particles interact in a range which is controlled by a kernel (smoothing) function, so that this kernel approximation for any two given particles, i and j , can be expressed by Eq. (2). ( ) ( ) ( , ) i j i j j f x f x W x x h dx     (2) where, the W in Eq. (2) is the smooth function which can be determined by Eq. (3). 1 ( , ) ( ) ( ) i j i j d i j W x x h x x h x x      (3) The i x and j x are the coordinates of the particles in the problem domain Ω and h is the distance between the two particles. The parameters d and θ in Eq. (2) represent the number of the space dimension and an auxiliary function, respectively (see 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Displacement [mm] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Load [kN] Specimen K1 Specimen K2 Specimen K3 Specimen K4 Specimen K5 M