Nonlinear elasticity in nanostructured materials

Abstract

We elaborate on a blended continuum/atomistic theoretical picture of the nonlinear elastic properties of nanostructured materials, looking at diverse aspects such as dispersions of inhomogeneities within a matrix, random or graded nanograined materials, two-dimensional atomic sheets. In particular, we discuss the possible onset of length-scale effects and we establish the limits and merits of continuum versus atomistics. While most situations here discussed correspond to model systems, the main conclusions have a paradigmatic relevance and indeed apply to most nanomaterials of current interest. This article was invited by S Washburn.

Strengthening metal nanolaminates under shock compression through dual effect of strong and weak graphene interface

“…It is observed that the interlayer stress reverses when shock wave reflects on the graphene interface, which can verify the approximate free boundary condition. Though the graphene is strongly nonlinear for relatively large strain, 2,25 it is found that the actual strain in graphene is small during the shock wave propagating due to the free boundary effect. Thus, the nonlinear effect here does not play an important role on the wave propagation, which is also consistent with the previous research about Kurdjumov-Sachs interface.…”

Thermal effects in magnetoelectric memories with stress-mediated switching

“…The coupling problem can be approached and solved by means of the multi-physics Eshelby formalism [32,31,30,15]. As recently verified [15], the local stress depends on the external electric and elastic fields and on the magnetization direction.…”

“…Nevertheless, we may now consider an arbitrary size of the particle. To explain this point we recall an important property of the Eshelby theory (which is valid for the case with any possible coupling): when an ellipsoidal particle is embedded in an infinite matrix and subjected to uniform external actions, the physical fields (electric, magnetic and elastic) induced within the particle itself are always uniform and they depend on the material properties of the two phases and on the ratios a 1 /a 2 and a 2 /a 3 [32,31,30,15,47,48,49]. The internal fields do not depend on the actual size of the particle: only the shape of the ellipsoid may influence the particle response.…”

“…The static behavior of the particle is described by a generalized energy function, able to allow for the spin-reorientation in terms of the applied electric field. Nanomechanical techniques [29,30], based on the multi-physics Eshelby theory [31,32], have been of primary importance for determining the distribution of the physical field within the heterogeneous structure. As for the dynamic response of the system, the above-mentioned analytical form of the energy function has been combined with classical ferromagnetic models [33,34], in order to obtain the evolution equation of the magnetization direction during the switching phases.…”

Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device

“…Equation (1) is valid for |σ| ≤ σ max . It is demonstrated in [2] and [3] that the material constant D depends on the direction considered on the graphene plane.…”