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Abstract:
Mode I fracture behavior of edge- and centrally-cracked nanobeams is analyzed by employing both stress-driven non-local theory of elasticity and Bernoulli–Euler beam theory. The present formulation implements the size-dependency experimentally observed at material micro- and nanoscale, by assuming a non-local constitutive law, that relates the strain to the stress in each material point of the body, through an integral convolution and a kernel. It is observed that the energy release rate decreases by increasing the nonlocality, showing the superior fracture performance of nanobeams with respect to large-scale beams.

Keywords:
energy release rate, nanobeam, stress-driven, non-local integral model, stress intensity factor

Abstract:
Free flexural vibrations of nanobeams with non-rigid edge supports are studied by means of the stress-driven nonlocal elasticity model and Euler-Bernoulli kinematics. The elastic deformations of the supports are modelled by transversal and flexural springs, so that, in the limit conditions when the springs stiffnesses tend to zero or infinity, the classical free, pinned, and clamped boundary conditions may be recovered. An analytical procedure is used to derive the closed form solution of the spatial differential equation. The problem of finding the natural frequencies is then reduced to find the roots of the determinant of a matrix, whose elements are explicitly given. The proposed technique, then, avoids the numerical instabilities usually arising when the numerical techniques are used to obtain the solution. The effects of both non-rigid supports elastic deformations and nonlocal parameter on the natural frequencies are studied also for higher vibrations modes. The comparison between the solutions of the proposed model and those available in the literature shows an excellent agreement, and new insightful results and discussions are presented.

Keywords:
elastically constrained beam, nanostructures, natural frequency, size effects, well-posed nonlocal formulation