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Abstract Crack advance from short or long pre-cracks is predicted by the progressive failure of a cohesive zone in a strain gradient, elasto-plastic solid. The presence of strain gradients leads to the existence of an elastic zone at the tip of a stationary crack, for both the long crack and the short crack cases. This is in sharp contrast with previous asymptotic analyses of gradient solids, where elastic strains were neglected. The presence of an elastic singularity at the crack tip generates stresses which are sufficiently high to activate quasi-cleavage. For the long crack case, crack growth resistance curves are predicted for a wide range of ratios of cohesive zone strength to yield strength. Remarkably, this feature of an elastic singularity is preserved for short cracks, leading to a severe reduction in tensile ductility. In qualitative terms, these predictions resemble those of discrete dislocation calculations, including the concept of a dislocation-free zone at the crack tip. [ABSTRACT FROM AUTHOR]

In the last decade there has been significant research activity in the use of Eringen’s nonlocal models to reformulate the equations of beams and plates. All of the previous works used a length scale parameter to study its effect on bending, buckling, and vibration characteristics, without identifying what the length scale parameter means. An attempt is made herein, for the first time, to relate the length scale parameter(s) to physical parameters. The Eringen’s non-local Euler–Bernoulli and Timoshenko beam models are identified as continuum limits of a discrete system comprising of harmonic oscillators. The correspondence between the coefficients of the discrete and the continuum models is used to determine the source of the non-locality in the context of Eringen’s non-local beams. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a new boundary treatment with almost second-order accuracy that does not require neighboring lattice information. In order to achieve improved accuracy for the boundary lattices, we used adaptive relaxation times reflecting boundary length scales that were unequal to the length scale of the internal fluid region lattices. Since the boundary treatment using adaptive relaxation times at the boundaries was formulated without information about the neighboring lattices, it could be easily applied to complex geometries. Numerical results using the proposed boundary treatment showed almost second-order accuracy for two-dimensional and three-dimensional problems without using information from neighboring lattices, unlike interpolation or extrapolation methods. [Copyright &y& Elsevier]