Related papers: Does elastic stress modify the equilibrium corner …
This study presents an analytical investigation of stress distributions in square-shaped elastic bodies subjected to concentrated compressive loads under uniaxial and biaxial conditions. By employing the Airy stress function method, we…
A consistent treatment of the coupling of surface energy and elasticity within the multi-phase- field framework is presented. The model accurately reproduces stress distribution in a number of analytically tractable, yet non-trivial, cases…
We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants.…
We introduce a modified Kirchhoff-Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. In a specific setting, we characterize quantitatively some properties of…
Understanding crystal growth over arbitrary curved surfaces with arbitrary boundaries is a formidable challenge, stemming from the complexity of formulating non-linear elasticity using geometric invariant quantities. Solutions are generally…
After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential…
A vector field similar to those separately introduced by Artstein and Dafermos is constructed from the tangent to a monotone increasing one-parameter family of non-concentric circles that touch at the common point of intersection taken as…
We put forward a variational framework suitable for the study of curves whose energies depend on their bend and twist degrees of freedom. By employing the material curvatures to describe such elastic deformation modes, we derive 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…
We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area…
The equations of stress equilibrium and strain compatibility/incompatibility are discussed for fields with point singularities in a planar domain. The sufficiency (or insufficiency) of the smooth maps, obtained by restricting the singular…
We study free-discontinuity functionals in nonlinear elasticity, where discontinuities correspond to the phenomenon of cavitation. The energy comprises two terms: a volume term accounting for the elastic energy; and a surface term…
In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers…
In a recent paper by Iglesias, Rumpf and Scherzer (Found. Comput. Math. 18(4), 2018) a variational model for deformations matching a pair of shapes given as level set functions was proposed. Its main feature is the presence of anisotropic…
Living cells respond to mechanical changes in the matrix surrounding them by applying contractile forces that are in turn transmitted to distant cells. We calculate the mechanical work that each cell performs in order to deform the matrix,…
Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional…
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…
We study critical surfaces for a surface energy which contains the squared $L^2$ norm of the difference of the mean curvature $H$ and the spontaneous curvature $c_o$, coupled to the elastic energy of the boundary curve. We investigate the…
We study the effect of large-scale spectral forcing on the scale-dependent anisotropy of the velocity field in direct numerical simulations of homogeneous incompressible turbulence. Two forcing methods are considered: the steady ABC single…
We present a new finite deformation, dynamic finite element model that incorporates surface tension to capture elastocapillary effects on the electromechanical deformation of dielectric elastomers. We demonstrate the significant effect that…