The paradox of smooth and abrupt bends in two-dimensional in-plane shear-crack mechanics |
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| Authors: | Taku Tada Teruo Yamashita |
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| Institution: | Earthquake Research Institute, the University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113, Japan |
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| Abstract: | It is pointed out, in the context of the boundary integral equation method (BIEM), that, in the mechanics of 2-D curved in-plane shear cracks, a smooth curve, along which the crack orientation changes continuously, and an abrupt kink, across which it changes discontinuously, are not equivalent to each other. The discrepancy is illustrated by numerical results, and a set of conceptual models is used to demonstrate analytically how the equations that govern the crack mechanics have inherently distinct forms depending on whether the crack orientation changes continuously or abruptly across a bend, as long as one abides by the principles of linear elasticity theory. This has serious implications for the numerical treatment of a curved crack, which can be modelled as a chain of finite elements that are connected either smoothly or at abrupt kinks, the two methods producing different numerical outcomes. No similar paradox arises in the cases of anti-plane shear or open in-plane cracks. |
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| Keywords: | cracks |
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