13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- a(x) =min(a0 1−D(x) ,d(x)) (6) where a(x) represents the radius of the sphere containing the integration points where the thermal expansion is imposed to reconstruct the interaction-based weigh function, a0 is a model parameter related to the maximum aggregate size, D is the local damage, d is the minimal distance from any boundary of the structure. 3.2. Dynamic failure of a rod This example is used to test the relevance of the proposed model and its capabilities to describe progressive failure and complete failure. A bar is submitted at both extremities to constant strain waves, which propagate toward the center in the linear elastic regime (see Fig. 5 and Table 1). When the two waves meet at the center, the strain amplitude is doubled, the material enters the softening regime suddenly, and failure occurs. In all computations, the time step is chosen to be equal to the critical time step. Table 1. Characteristics of the rod dynamic failure test Parameter L v E ρ lc/a0 εD0 αt At Bt αc Unit cm cms−1 MPa kgm-3 cm Value 30 0.7 1 1 4 1 1 1 2 0 Figure 5. Dynamic failure of a rod: test description and time evolution of the strain amplitude repartition along the rod. In the course of damage, the crack opening displacement (COD) can be estimated using the method proposed by [26] and compared to an ideal crack opening profile obtained from a strong discontinuity analysis (single crack). The comparison, e.g., the distance between the two profiles, indicates how close the strain and damage distributions are from those corresponding to a single crack surrounded by a fracture process zone. Details may be found in [13] based on [26]. Figure 6. Dynamic failure of a rod (Reproduced from [25]): (left) distance between the computed COD and an ideal opening profile obtained for a strong discontinuity versus time; (right) strain in the cracked element versus adimensional element size at complete failure.
RkJQdWJsaXNoZXIy MjM0NDE=