Abstract
The J-integral, which is crucial to the nonlinear fracture analysis within the framework of continuum fracture mechanics, fails at the atomic scale due to the atomic discreteness emerging with decreasing size. In this paper, a novel atomic J-integral calculation method is proposed for atomically sharp cracks by developing a new integral scheme to describe the local displacement gradient and stress field for discrete models. The applicability of the atomic J-integral is verified by comparing with traditional FEM and stress-based method, and its path-independency is elucidated by evaluating the geometric nonlinearity at the atomic scale. Furthermore, it is corroborated that the atomic J-integral method is dimension-independent even at the ultra-small scale below the dimensional limit of continuum mechanics.
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