In this paper, we examine the existence of conditions that the mode II crack extensions occur under compressive loads. It is important to elucidate the fracture criterions under compressive loads such as the explanation of the existence and the creation of long faults, landslide in slope ground and so on. We find, by using the maximum energy release rate criterion, that the mode II crack extensions occur by the shear stress with the necessary parallel compressive stresses for a crack surface. We also find that the mode II crack extensions do not occur by the well-known maximum stress criterion
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