We probe the local mechanical properties of microtubules at the nanometer scale by radial indentation with a scanning force microscope tip. We find a linear elastic regime that can be described by both thin-shell theory and finite element methods, in which microtubules are modeled as hollow tubes. We also find a nonlinear regime and catastrophic collapse of the microtubules under large loads. T...

The peridynamic model of solid mechanics is a nonlocal theory containing a length scale. It is based on direct interactions between points in a continuum separated from each other by a finite distance. The maximum interaction distance provides a length scale for the material model. This paper addresses the question of whether the peridynamic model for an elastic material reproduces the classica...

In compressible Neohookean elasticity one minimizes functionals which are composed by the sum of the L2 norm of the deformation gradient and a nonlinear function of the determinant of the gradient. Non–interpenetrability of matter is then represented by additional invertibility conditions. An existence theory which includes a precise notion of invertibility and allows for cavitation was formula...

Abstract We provide an approximation result for the pure traction problem of linearized elasticity in terms local minimizers finite elasticity, under constraint vanishing average curl admissible deformation maps. When suitable rotations are included constraint, limit is shown to be linear elastic equilibrium associated rotated loads.

The elastic properties of a molecule of duplex DNA are strongly dependent on nucleotide sequence. In the theory developed here the contribution c of the nth base-pair step to the elastic energy is assumed to be given by a function c̃ of six kinematical variables, called tilt, roll, twist, shift, slide, and rise, that describe the relative orientation and displacement of the nth and (n11)th base ...

Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt heterojunctions and interfaces. The conventional interface boundary conditions, often referred to as ‘‘connection rules,’’ require that the displacement field and its as...

c = c = c . (2) 1 We use the notation of Schouten [9]. Symmetrization over two indices is denoted by parentheses, A(ij) := (Aij + Aji)/2!, antisymmetrization by brackets, B[ij] := (Bij − Bji)/2!. The analogous is valid for more indices, as, e.g., in (13): c i[jk]l = (c − c)/2!. If one or more indices are exempt from (anti)symmetrization, they are enclosed by vertical bars, as, e.g., in (12), c ...

In this article, finite difference method (FDM) is used to solve sixth-order derivatives of differential equations in buckling analysis of nanoplates due to coupled surface energy and non-local elasticity theories. The uniform temperature change is used to study thermal effect. The small scale and surface energy effects are added into the governing equations using Eringen’s non-local elasticity...