Search results for "Elasticity"

Spectral analysis of the Neumann-Poincaré operator and characterization of the stress concentration in anti-plane elasticity

2012

When holes or hard elastic inclusions are closely located, stress which is the gradient of the solution to the anti-plane elasticity equation can be arbitrarily large as the distance between two inclusions tends to zero. It is important to precisely characterize the blow-up of the gradient of such an equation. In this paper we show that the blow-up of the gradient can be characterized by a singular function defined by the single layer potential of an eigenfunction corresponding to the eigenvalue 1/2 of a Neumann–Poincare type operator defined on the boundaries of the inclusions. By comparing the singular function with the one corresponding to two disks osculating to the inclusions, we quant…

A theoretical link between gradient and nonlocal elasticity models, including higher order boundary conditions

2013

The paper presents a recently developed rational derivation of the strain gradient elasticity model from the nonlocal (or integral) model. This kind of derivations are generally recovered just by an expansion into a Taylor series of the nonlocal strain field up to a certain order, and then operating the integration (or averaging) over the spatial interaction domain. The latter procedure is fully consistent when the analysis is performed over an unbounded domain, but when a classical bounded domain is analyzed it lacks in reproducing the so-called higher-order boundary conditions. In the present contributions the complete derivation is achieved employing an extended version of the Principle …

Hellinger-Reissner variational principle for stress gradient elastic bodies with embedded coherent interfaces

2017

An Hellinger-Reissner (H-R) variational principle is proposed for stress gradient elasticity material models. Stress gradient elasticity is an emerging branch of non-simple constitutive elastic models where the infinitesimal strain tensor is linearly related to the Cauchy stress tensor and to its Laplacian. The H-R principle here proposed is particularized for a solid composed by several sub-domains connected by coherent interfaces, that is interfaces across the which both displacement and traction vectors are continuous. In view of possible stress-based finite element applications, a reduced form of the H-R principle is also proposed in which the field linear momentum balance equations are…

Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method

2021

AbstractIn this study, an innovative procedure is presented for the analysis of the static behavior of plates at the micro and nano scale, with arbitrary shape and various boundary conditions. In this regard, the well-known Eringen’s nonlocal elasticity theory is used to appropriately model small length scale effects. The proposed mesh-free procedure, namely the Line Element-Less Method (LEM), only requires the evaluation of simple line integrals along the plate boundary parametric equation. Further, variations of appropriately introduced functionals eventually lead to a linear system of algebraic equations in terms of the expansion coefficients of the deflection function. Notably, the prop…

Exact mechanical models of fractional hereditary materials

2012

Fractional Viscoelasticity is referred to materials, whose constitutive law involves fractional derivatives of order β R such that 0 β 1. In this paper, two mechanical models with stress-strain relation exactly restituting fractional operators, respectively, in ranges 0 β 1 / 2 and 1 / 2 β 1 are presented. It is shown that, in the former case, the mechanical model is described by an ideal indefinite massless viscous fluid resting on a bed of independent springs (Winkler model), while, in the latter case it is a shear-type indefinite cantilever resting on a bed of independent viscous dashpots. The law of variation of all mechanical characteristics is of power-law type, strictly related to th…

2019

Atomic force microscopy (AFM) is today an established tool in imaging and determination of mechanical properties of biomaterials. Due to their complex organization, those materials show intricate properties such as viscoelasticity. Therefore, one has to consider that the loading rate at which the sample is probed will lead to different mechanical response (properties). In this work, we studied the dependence of the mechanical properties of endothelial cells on the loading rate using AFM in force spectroscopy mode. We employed a sharp, four-sided pyramidal indenter and loading rates ranging from 0.5 to 20 μm/s. In addition, by variation of the load (applied forces from 100 to 10,000 pN), the…

Measuring (biological) materials mechanics with atomic force microscopy. 2. Influence of the loading rate and applied force (colloidal particles)

2020

Atomic force microscopy (AFM) is the most often used tool to study the mechanical properties of eukaryotic cells. Due to their complex assembly, cells show viscoelastic properties. When performing experiments, one has to consider the influence of both loading rate and maximum load on the measured mechanical properties. Here, we employed colloidal particles of various sizes (from 2 to 20 μm diameter) to perform force spectroscopy measurements on endothelial cells at loading rates varying from 0.1 to 50 μm/s, and maximum loads ranging from 1 to 25 nN. We were able to determine the non-linear dependence of cell viscoelastic properties on the loading rate which followed a weak power law. In add…

Maximizing phonon thermal conductance for ballistic membranes

2007

At low temperatures, phonon scattering can become so weak that phonon transport becomes ballistic. We calculate the ballistic phonon conductance G for membranes using elasticity theory, considering the transition from three to two dimensions. We discuss the temperature and thickness dependence and especially concentrate on the issue of material parameters. For all membrane thicknesses, the best conductors have, counter-intuitively, the lowest speed of sound.

Nucleation and accretion of bioelastomeric fibers at biological temperatures and low concentrations.

1988

Quasi-elastic light scattering (QELS) studies are reported, which address the early stages of aggregation of the polypentamer poly(VPGVG). This reflects the major primary structural feature of native elastin. The study is focused on the region of the phase diagram which in both its temperature and concentration range is closest to the state of affairs occurring in the course of bioelastogenesis by progressive synthesis of the precursor protein. Results here reported allow for the first time a self-consistent view of the physics of elastogenesis, and specify the role of the region of metastability and of that of instability of the phase diagram in the non-chaotic, orderly formation of elasto…

Hydration dependent dynamics in sol-gel encapsulated myoglobin.

2008

In this work we study the effect of hydration on the dynamics of a protein in confined geometry, i.e. encapsulated in a porous silica matrix. Using elastic neutron scattering we investigate the temperature dependence of the mean square displacements of non-exchangeable hydrogen atoms of sol-gel encapsulated met-myoglobin. The study is extended to samples at 0.2, 0.3 and 0.5 g water/g protein fractions and comparison is made with met-myoglobin powders at the same average hydration and with a dry powder sample. Elastic data are analysed using a model of dynamical heterogeneity to take into account deviations of elastic intensity from gaussian behaviour in a large momentum transfer range and r…