![]() ![]() Weibull 4 first explains the scale effect based on the weakest link theory. For this reason, it is impossible to treat global behavior by means of a local law 3. Therefore, the fracture in these kinds of materials constitutes a cooperative and multiscale problem, and where the phenomenon becomes critical, other length scales start to play an important role 2. The micro-crack interacts in a complex way because it produces at the end of the damage process the nucleation of one or more macro-cracks that determine the rupture of the structure under study. This process must consider the scale effect when determining the mechanical parameters involved, the random nature of the mechanical properties, and the phenomenon of micro-cracks interaction. A complex fracture process characterizes the collapse in quasi-brittle materials. However, the study of the damage evolution and the rupture in quasi-brittle materials is an area where consistent calculation methodologies do not yet exist 1. These materials characterize the nonlinear mechanical behavior governed by clouds of micro-cracks that interact and grow in size and intensity. Problems of practical interest in engineering in the most varied scales are inherently related to the knowledge of the damage evolution in quasi-brittle materials such as ceramics, concrete, and rocks, among others. Understand better some aspects of the size effect using the numerical tool and show that the Lattice Discrete Element Method has enough robustness to be applied in the nonlinear analysis of structures built by quasi-brittle materials. ![]() Two main aspects appear as a result of the analysis presented here. Its results allow the researchers to see the connection between the numerical results regarding the size effect and the theoretical law based on the fractal dimension of the parameter studied. In the present work, a version of the Discrete Element Method is used to simulate the mechanical behavior of different size specimens until collapse by analyzing the size effect represented by this method. Moreover, it can also help to relax the continuum hypothesis. This method can allow failures with relative ease. On the other hand, the Discrete Method is an interesting option to be used in the simulation collapse process of quasi-brittle materials. Some aspects of the scaling law based on the fractal concepts proposed by Prof Carpinteri are analyzed in this work. This process also governs the size effect, that is, the changes of the global parameters as the strength and characteristic strain and energies when the size of the structure changes. The interaction among clouds of micro-cracks generates the localization process that implies transforming a continuum domain into a discontinue one. When damage is produced, two phenomena can take place: the damage produced governs the collapse process when working with this type of material, and its random nature rules the nonlinear behavior up to the collapse. Nowadays, there are many applications in the field of Engineering related to quasi-brittle materials such as ceramics, natural stones, and concrete, among others. ![]()
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