Related papers: Large deformations of gradient elastic beams
"Granular elasticity," useful for calculating static stress distributions in granular media, is generalized by including the effects of slowly moving, deformed grains. The result is a hydrodynamic theory for granular solids that agrees well…
In our analysis, we show that Efrati et al.'s publication is inconsistent with the mathematics of plate theory. However it is more consistent with the mathematics of shell theory, but with an incorrect strain tensor. Thus, the authors'…
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
By means of a variational approach we rigorously deduce three one-dimensional models for elastic ribbons from the theory of von K\'arm\'an plates, passing to the limit as the width of the plate goes to zero. The one-dimensional model found…
We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…
Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…
We study analytically the development of gravitational instability in an expanding shell having finite thickness. We consider three models for the radial density profile of the shell: (i) an analytic uniform-density model, (ii) a…
Networks of semiflexible or stiff polymers such as most biopolymers are known to deform inhomogeneously when sheared. The effects of such non-affine deformation have been shown to be much stronger than for flexible polymers. To date, our…
In the present work, the overall nonlinear elastic behavior of a 1D multi-modular structure incorporating possible imperfections at the discrete (micro-scale) level, is derived with respect to both tensile and compressive applied loads. The…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
The paper presents a micromechanical representation of deformation in 2D granular materials. The representation is a generalization of K. Bagi's work and is based upon the void-cell approach of M. Satake. The general representation applies…
The stability of a sheared magnetic field is analyzed in two-dimensional magnetohydrodynamics with resistive and viscous dissipation. Using a multiple-scale analysis, it is shown that at large enough Reynolds numbers the basic state…
A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of…
We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
The three-dimensional axisymmetric Boussinesq problem of an isotropic half-space subjected to a concentrated normal quasi-static load is studied within the framework of linear dipolar gradient elasticity. Our main concern is to determine…
In \cite{Lei}, the author derived an exact rotation-strain model in two dimensions for the motion of incompressible viscoelastic materials via the polar decomposition of the deformation tensor. Based on the rotation-strain model, the author…
The experimental observations of many interaction-driven electronic phases in moir\'e superlattices have stimulated intense theoretical and experimental efforts to understand and engineer these correlated physics. Strain is a powerful tool…
We study the elasto-plastic behaviour of materials made of individual (discrete) objects, such as a liquid foam made of bubbles. The evolution of positions and mutual arrangements of individual objects is taken into account through…
Two dimensional simulations of non-cohesive granular matter in a biaxial shear tester are discussed. The effect of particle elasticity on the mechanical behavior is investigated using two complementary distinct element methods (DEM): Soft…