Related papers: Elastic energy of a straight dislocation and contr…
We study interactions between biological cells that apply anisotropic active mechanical forces on an elastic substrate. We model the cells as thin discs that along their perimeters apply radial, but angle-dependent forces on the substrate.…
We propose a model for rate-independent evolution in elastoplastic materials under external loading, which allows large strains. In the setting of strain-gradient plasticity with multiplicative decomposition of the deformation gradient, we…
Non-singular dislocation continuum theories are studied. A comparison between Peierls-Nabarro dislocations and straight dislocations in strain gradient elasticity is given. The non-singular displacement fields, non-singular stresses,…
Our first-principles calculations show that both the compressional and shear waves of hcp-Fe become elastically isotropic under the high temperatures of Earth inner core conditions, with the variation in sound velocities along different…
The linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates. For the generated forces, stress and displacement fields, we find strong…
A simple model of inelastic hard-rods subject to a one-dimensional array of identical wells is introduced. The energy loss due to inelastic collisions is balanced by the work supplied by an external stochastic heat-bath. We explore the…
For homogeneous and isotropic linearly elastic solids and for incompressible fluids under low-Reynolds-number conditions the fundamental solutions of the associated continuum equations were derived a long time ago for bulk systems. That is,…
We consider a variational anti-plane lattice model and demonstrate that at zero temperature, there exist locally stable states containing screw dislocations, given conditions on the distance between the dislocations, and on the distance…
Application of isotropic pressure or uniaxial strain alters the elastic properties of materials; sufficiently large strains can drive structural transformations. Linear elasticity describes stability against infinitesimal strains, while…
In solids, external stress induces the Peach-Koehler force, which drives dislocations to move. Similarly, in liquid crystals, an external angular stress creates an analogous force, which drives disclinations to move. In this work, we…
We consider the energetic description of a visco-plastic evolution and derive an existence result. The energies are convex, but not necessarily quadratic. Our model is a strain gradient model in which the curl of the plastic strain…
The effect of interstitial hydrogen on the elastic properties of $\alpha$-iron is investigated using \textit{ab initio} density functional theory. We find that while the overall strength properties are reduced by H, the effects are mainly…
In the modeling of dislocations one is lead naturally to energies concentrated on lines, where the integrand depends on the orientation and on the Burgers vector of the dislocation, which belongs to a discrete lattice. The dislocations may…
The strain states of the components of pseudomorphic superlattices can be accurately modeled analytically through the application of linear elasticity. In this particular case of GaN/AlN 'free-standing' superlattices, the predictions…
We compute the relaxation of the total energy related to a variational model for nematic elastomers, involving a nonlinear elastic mechanical energy depending on the orientation of the molecules of the nematic elastomer, and a nematic…
Earth's inner core consists of mainly iron with a bit of light elements. Understanding of its structure and related physical properties has been elusive for both experiment and theory due to its required extremely high pressure and…
We reformulate the theory of polycrystalline plasticity, in externally driven, nonequilibrium situations, by writing equations of motion for the flow of energy and entropy associated with dislocations. Within this general framework, and…
A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each…
We investigate the effects of dissipative air drag on the dynamics of electrified jets in the initial stage of the electrospinning process. The main idea is to use a Brownian noise to model air drag effects on the uniaxial elongation of the…
We are concerned with a variant of the isoperimetric problem, which in our setting arises in a geometrically nonlinear two-well problem in elasticity. More precisely, we investigate the optimal scaling of the energy of an elastic inclusion…