Issue 36

A. Namdar et alii, Frattura ed Integrità Strutturale, 36 (2016) 168-181; DOI: 10.3221/IGF-ESIS.36.17 170 Subsequently can write:          1 C D       where the elastic compliance matrix, [ ] D , is given by inverse of matrix   C   1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 2 1 0 0 0 0 0 2 1 0 0 0 0 0 2 D E                                             According to [16], the strain can be categorized under three types which are; Natural or true strain;   0 0 ln l l dl l l l           Engineering strain;   0 l l    Hooke’s law strain;   E    The Hooke’s law strain has been used in numerical simulation giving a linear stress-strain relationship. This strain energy density is the required energy to deforming the material. Fracture toughness is the elastic strain energy density known as resilience and it is defined as 0 W d      , this expression represents an elastic behavior up to the yield strain [16]. M ODELING SETUP FOR NUMERICAL SIMULATION he crack mode is an important issue in fracture mechanics. The crack can be categorized in three modes; mode 1: opening or tensile mode, mode 2: sliding or in-plane shear mode, mode 3: out of plane tearing. In this paper tensile mode (mode 1) has been simulated. The tensile mode is the most common mode where crack occurs on the plane characterized by maximum tensile stress. The cases of failure are typical crack under tensile mode with different length, start at center of calibrated length beam, initiating at the bottom and ending at the top. The fracture toughness of beam, with resist progressive tensile crack extension has been modeled considering linear elastic fracture mechanics concept. The stress intensity modification in developing crack was numerically simulated, and crack development and stress intensity are studied. The Material properties have been referred to literature, and cracking moment design calculated according to ACI code. The cracking moment is applied on the beam. The mechanical property of ultra-high strength concrete (UHPC) and normal strength concrete (NSC) have been indicated in Tab. 1. The SI units have been used in numerical simulation (Tab. 2). Three steps have been made in crack development on body of plain concrete beam. The crack started in 25 % of beam length from bottom and subsequently up to 50 % and finally fully cracked and collapsing. At each stage crack remain stable in order to understand of the beam mechanism failure. The geometry and boundary condition are shown in Figs. 1-2. Specimen Young’s modulus (MPa) Poisson’s ratio Ultimate strength (MPa) Ultimate strain Density (kg/m 3 ) NSC 49,195 0.24 56.6 0.0014 2440.5 UHPC 51,503 0.20 128.9 0.0025 2424.9 Table 1 : Concrete material properties for elastic analyses [17]. T