Related papers: Does elastic stress modify the equilibrium corner …
We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…
Relating microstructure to properties, electromagnetic, mechanical, thermal and their couplings has been a major focus of mechanics, physics and materials science. The majority of the literature focuses on deriving homogenized constitutive…
Using molecular-dynamics simulation and finite-element modelling, we simulate nanoindentation into the three principal surfaces -- the (100), (110) and (111) surface -- of Cu and Al. In the elastic regime, the simulation data agree fairly…
The contact between a liquid and an elastic solid generates a stress vector depending on the curvature tensor in each point of the separating surface. For nanometer values of the mean curvature and for suitable materials, the stress vector…
Some issues that arise when modeling elastic energy for binary alloys are discussed within the context of a Keating model and density functional calculations. The Keating model is based on atomistic modeling of elastic interactions in…
A signature of the dark energy equation of state may be observed in the shape of voids. We estimate the constraints on cosmological parameters that would be determined from the ellipticity distribution of voids from future spectroscopic…
Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of…
We consider models for elastic liquids, such as solutions of flexible polymers. They introduce a relaxation time $\lambda$ into the system, over which stresses relax. We study the kinematics of the problem, and clarify the relationship…
The energy-based definition provides a viable resolution to the longstanding confusion on the proper definition of $n$-th order rigidity and flexibility in geometric constraint systems. Applying an energy-based local rigidity analysis to…
In materials that undergo martensitic phase transformation, macroscopic loading often leads to the creation and/or rearrangement of elastic domains. This paper considers an example {involving} a single-crystal slab made from two martensite…
In this paper we derive an obstacle problem with a free boundary to describe the formation of voids at areas of intense geological folding. An elastic layer is forced by overburden pressure against a V-shaped rigid obstacle. Energy…
Vertex models have been extensively used for simulating the evolution of multicellular systems, and have given rise to important global properties concerning their macroscopic rheology or jamming transitions. These models are based on the…
This article is devoted to investigate the singular profile of the free boundary of two-dimensional incompressible inviscid fluid with external force near the stagnation point. More precisely, given an external force with some polynomial…
Bifurcation of an elastic structure crucially depends on the curvature of the constraints against which the ends of the structure are prescribed to move, an effect which deserves more attention than it has received so far. In fact, we show…
Computing equilibrium shapes of crystals (ESC) is a challenging problem in materials science that involves minimizing an orientation-dependent (i.e., anisotropic) surface energy functional subject to a prescribed mass constraint. The highly…
Surface tension is a prominent factor for the deformation of solids at micro-/nano-scale. This paper investigates the effects of surface tension on the two-dimensional contact problems of an elastic layer bonded to the rigid substrate.…
Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk…
By introducing the divergence of a vector potential into the Lagrangian, a Lagrangian framework is developed to incorporate surface energy into elasticity. Besides the Euler-Lagrange equation and natural boundary condition, a new boundary…
Numerical simulations on a 2-dimensional model system showed that voids are induced primarily due to shape anisotropy in binary mixtures of interacting disks. The results of such a simple model account for the key features seen in a variety…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…