DYNAMIC FRACTURE SOLID FRAGILE: COMPARISON OF DISCRETE MODELS WITH THE THEORY OF CONTINUOUS
Summary: This thesis has developed a model of discrete dynamic fracture imp] ementado by a code similar to those of dynamic mo] ECU] with ar e] to analyze various aspects of the dynamics of a fracture that is spread by a matter] fragile . The first and second derivative appearing in the equation] to linear elasticity, have been estimated using a method of optimization to six neighbors has led to an expression of discrete equations of elasticity online] in a triangular network. Likewise has propyesto a criterion of fracture imp] ementado on nodes] to network, which is the criterion used to determine when a piece of art] is disconnected from the rest. Later has been ac or a study of the characteristics of] art] represented by the equations of discretizadas] to linear elasticity and have determined the dispersion relations for this material. Then have analyzed the characteristics of the fracture patterns obtained from the simulations. First, it has gained the field distortion that exists at the plate for] a static situation, being that this area corresponds qualitatively with the field asymptotic allowed to make comparisons] field obtained in the simulation with the theoretical expressions. Secondly has conducted an analysis] to kinematics of a broken bearing in mind the temporal evolution of] speed of the tip of the fracture and its acceleration. E] behavior of both magnitudes coincides with the qualitatively described in experiments on fragile materials. Subsequently has studied the speed of branching and dependence] length] to show begins] practiced in] board. Values have been found for such speed branching who are within the range of those obtained experimentally. Finally, we have identified two mechanisms branching: one associated with the instability dynamics, and that is] that produces the first branching, and a second mechanism (responsab] e] a second branching) associated with the arrival at the tip ] fracture of surface waves generated in the first event of disconnection and subsequently reflected in e] free upper edge of the plate. In conclusion e] traajo there has been a qualitative explanation of instability in which branching is evident that when a crack propagates by half discreet whose area of deformation due t] asymptotic field, the temporal evolution of this field the address line as well as in the lateral direction with respect to movement of rectilinear] to tip is such that for certain values of the speed of the tip of the fracturea status fracture threshold was sumple earlier in the lateral direction in which] to address straight and thus branching occurs.
