A Nonlocal Finite Element Approach to Nanobeams

This paper presents a consistent derivation of a new nonlocal finite element procedure in the framework of continuum mechanics and nonlocal thermodynamics for the analysis of bending of nanobeams under transverse loads. This approach is able to provide the overall performance and the influence of specific parameters in the behavior of nanobeams and it is also able to deal with nanomechanical systems by solving a reduced number of algebraic equations. An example shows that the proposed nonlocal finite element procedure, using a mesh composed by only four elements of equal size, provides the exact values in terms of transversal displacement and bending of the nanobeam

A finite element for nonlocal elastic analyses

A nonlocal elastic behaviour of integral type is modeled assuming that the nonlocality lies in the constitutive relation. The diffusion processes of the nonlocality are governed by an integral relation containing a recently proposed symmetric spatial weight function expressed in terms of an attenuation function. Starting from the variational formulation associated with the structural boundary-value problem in the context of nonlocal elasticity, a nonlocal finite element model is proposed and a 1D example is proposed

Variational formulations, convergence and stability properties in nonlocal elastoplasticity

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Second gradient poromechanics

International audienceSecond gradient theories have been developed in mechanics for treating different phenomena as capillarity in fluids, plasticity and friction in granular materials or shear band deformations. Here, there is an attempt of formulating a second gradient Biot like model for porous materials. In particular the interest is focused in describing the local dilatant behaviour of a porous material induced by pore opening elastic and capillary interaction phenomena among neighbouring pores and related micro-filtration phenomena by means of a continuum microstructured model. The main idea is to extend the classical macroscopic Biot model by including in the description second gradient effects. This is done by assuming that the surface contribution to the external work rate functional depends on the normal derivative of the velocity or equivalently assuming that the strain work rate functional depends on the porosity and strain gradients. According to classical thermodynamics suitable restrictions for stresses and second gradient internal actions (hyperstresses) are recovered, so as to determine a suitable extended form of the constitutive relation and Darcy's law. Finally a numerical application of the envisaged model to one-dimensional consolidation is developed; the obtained results generalize those by Terzaghi; in particular interesting phenomena occurring close to the consolidation external surface and the impermeable wall can be described, which were not accounted for previously

A Nonlocal Model for Carbon Nanotubes under Axial Loads

Various beam theories are formulated in literature using the nonlocal differential constitutive relation proposed by Eringen. A new variational framework is derived in the present paper by following a consistent thermodynamic approach based on a nonlocal constitutive law of gradient-type. Contrary to the results obtained by Eringen, the new model exhibits the nonlocality effect also for constant axial load distributions. The treatment can be adopted to get new benchmarks for numerical analyses