Structural interfaces in linear elasticity. Part I: Nonlocality and gradient approximations

Soft Neutral Elastic Inhomogeneities with Membrane-type Interface Conditions

“…The existing solutions of neutral inhomogeneities which make use of an appropriately designed homogeneous and continuous interphase in achieving neutrality can be divided into two main categories: (a) Those in which neutrality is achieved by introducing an interphase of arbitrary thickness between the inhomogeneity and the host solid, (b) Those in which neutrality is achieved by the construction of an imperfect interface which models a thin interphase between the inhomogeneity and the host solid. Another approach is that of Bertoldi et al [21], who introduce the concept of a "structural interphase" consisting of discrete truss elements, and study neutral inhomogeneities in that setting. The coated sphere assemblages of Hashin [22] and Hashin and Shtrikman [23] in which use is made of the neutrality concept of a coated sphere, and the coated ellipsoid assemblages of Benveniste and Milton [24] fall in Category (a).…”

A discrete-fibers model for bridged cracks and reinforced elliptical voids

“…Employing this setting, and expanding in Taylor series the solution (given by Eq. (11), see also Appendix C of Bertoldi et al, 2007a) for the infinite matrix with an elliptical hole loaded as in Fig. 7 near r ¼ 0 and near r ¼ 0, we obtain the leading-order terms of the displacement and stress fields near the crack tip (for b=a51) in terms of stress intensity factors K I and K II Mode I …”

“…Note that the displacements, and therefore the tractions transmitted by the fibers to the infinite matrix at the junctions, have an initially unknown distribution. Problem (3) is an example of a multistructure (see Kozlov et al, 1999 and references cited therein); a simplification of it is pursued here by working with averaged quantities at the junctions between the fibers and the infinite matrix, as explained in detail by Bertoldi et al (2007a). Briefly, we introduce the averaged tractions and displacements at junctions as …”

“…The solution for an infinite matrix containing an elliptical hole on which N piecewise uniform traction distributions having normal and tangential components p k and s k act on the parts z À k z þ k _ , see Fig. 3 (with null total resultant) is given by Bertoldi et al (2007a) where the polar form for z is used…”

Free vibration of nanorings/arches based on nonlocal elasticity

“…[12][13][14][15][16][17] As experiments at the nanoscale are extremely difficult and atomistic computations remain prohibitively expensive for large size atomic systems, continuum models continue to play an essential role in the study of nanostructures. [18][19][20][21][22][23][24] However, there are strong evidences [25][26][27][28][29] that the small length scale effect ͑i.e., nonlocal effect͒ has a significant influence on the mechanical behavior of nanostructures. Therefore, classical structural theories need to be modified to account for the small length scale effect if they are to be used.…”