Issue34

L. E. Kosteski et alii, Frattura ed Integrità Strutturale, 34 (2015) 226-236; DOI: 10.3221/IGF-ESIS.34.24 230 In the special case of an isotropic continuum with 0.25   , the value of the coefficients shown above are 1.125   and 0.4   , which lead to     * * /  /    0.34 l l d d A A A A   . Thus, for practical purposes, a single value of the critical length can be used for longitudinal and diagonal elements. Therefore, the stability condition is expressed by Eq. 16 and the limit strain by Eq. 17. 1 cr r i cr i L K L L L           (16) r r p K    (17) The random distribution of material parameters in the LDEM environment is modelled, defining the toughness, f G , as a random field with a Type III (Weibull) extreme value distribution. Details of the implementation can be found in Kosteski et al [12]. Figure 2 : (a) Layout and boundary condition of the rectangular plate with central fissure and imposed constant strain velocity; (b) The mechanical properties adopted for the LDEM model; (c) The constitutive uniaxial law adopted for the bars; (d) The characteristic of the analyzed cases. F IRST APPLICATION : SIMULATION OF CRITICAL CRACK PROPAGATION IN FUNCTIONAL GRADED MATERIALS he present example shows a rectangular plate of Polimetilmetacrilate (PMMA) with a central fissure. The plate dimensions are show in Fig. 2.a. This plate is submitted to constant strain velocity of 5m/s in its borders. Paulino and Zhang [2] studied the influence that the Functionally Graded Material (FGM) has in dynamic crack propagation in this same geometry using the Finite Element Method with cohesive interfaces. The cohesive elements were implemented in the region where fissure propagation could take place. The quoted authors studied the influence of three different types of FGM in the crack propagation event. In case 1 the homogeneous property was considered. In case 2 a hypothetic FGM material was proposed, where just the cohesive properties graded linearly in y axis direction. Finally, in case 3 not only the cohesive properties, but also the finite element properties were graded. DEM Model Only the middle of the plate was modeled due to the geometry and load symmetries of the problem. The plate was discretized with 60 modules on each side and one module in the thickness direction. The boundary conditions applied permit to represent the left border as a symmetry axis. The plane strain condition was imposed fixing the displacements in T