2d Frame Analysis V2 Crack -

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the orientation of the average failure plane seems to be almost horizontal. this figure shows that the orientation of the average failure plane at each confining pressure is almost constant and this orientation is almost constant with time. it indicates that the orientation of the average failure plane is almost independent of the strength of the confining pressure. this phenomenon can be interpreted as follows: at different confining pressures, by using the same amount of stress, the bulk material starts to crack at a different location. in this case, the average of the different positions of crack initiation forms the orientations of macroscopic failure planes. in this study, by using a linear elastic finite element code, it has been shown that the average orientation of the failure plane increases with increase in the amount of confining pressure. in addition, because of the no-zero v-axis normal force at zero stress, the applied stress is always directed to the left hand side in an isotropic material. therefore, in the bulk material, the stress is distributed uniformly in three directions (tangential, normal and v-axis direction). by increasing the amount of confining pressure, the main contribution of the tangential stress relative to the normal and the v-axis direction increases. as a result, the average orientation of the failure plane increases with increase in the amount of confining pressure. this result shows that the orientation of the average failure plane is almost independent of the amount of confining pressure. in other words, the average orientation of the failure plane has almost a constant value. d8a7b2ff72

the cases using the hydrofragmentation procedure for the uhv loading mode, as mentioned in the main text of this article, are illustrated by comparing the (curves) of figure 3c and 4c for 50k iterations. the images are digitized with an sem and their corresponding 3d models are obtained using matlab r2012a. the curvature of a curve is calculated by fitting the 3d model to each pixel of the digitalized sem image. the shapes and sizes of the powder particles and cracks were used as typical sizes for simulation of the resulting particles and cracks using nanofe. the final sem image for a similar case is shown in figure 5. even though the tool allows varying surface properties of particles and cracks, the values used in this study are the default ones.

current research is focused on understanding the dynamic fracture behavior of 2d frames under cyclic loading and what is the optimum shape of the frames, such as angles, length, etc. to model this problem, an array of 2d frames is used to simulate the fracture behavior of a sample. due to the complicated problem, the cracking process of the frames is simulated in a special manner and this simulation is called hydrofragmentation process. every particle, representing a frame element, is considered as a crack that is fully stretched along the edges of the particles. therefore the area of the particle can change from zero to almost maximum size during the cracking process. the intensity of the particle is considered based on its size. at the beginning of the simulation, all of the particles are equal (empty state). the cracks that are in contact with other cracks are automatically considered as pinned cracks and are used as reference point for the whole simulation. in order to calculate the relative friction angle of the particles, the basic models of hydrofragmentation are then used. this process iterates over each frame in the sample (size: ) for a given number of iterations (time: ). the frame is considered as totally cracked only when no particle remains in its original state (less than 10). therefore the maximum number of iterations is 200k with 50k being the chosen number of iteration for this optimization process.