Under mechanical deformation, most materials exhibit both elastic and fluid (or plastic) responses. No existing formalism derived from microscopic principles encompasses both their fluid-like and solid-like aspects. We define the statistical texture tensor to quantify the intuitive notion of stored deformation. This tensor links microscopic and macroscopic descriptions of the material, and exte...

We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in crystalline defects. The elastic heterogeneities are modeled as a second component with reduced elastic parameters. Using simulated annealing Monte Carlo simulations...

We develop an analytic and environment-dependent interatomic potential for the overlap repulsion in solid argon, based on an approximate treatment of the non-orthogonal Tight-Binding theory for the closed-shell systems. The present model can well reproduce the observed elastic properties of solid argon including Cauchy violation at high pressures, yet very simple. A useful and novel analysis is...

Motivated by recent experimental work that shows that the orientation dependence of the stiffness of steps on Cu surfaces differs significantly from the predictions of Ising and solid-on-solid modes, we study the effect of elastic anisotropy on the stiffness of steps on (1 0 0), (1 1 0) and (1 1 1) surfaces of cubic materials. The contribution to the stiffness due to elastic relaxation is obtai...

The level set method provides a natural framework for modelling multiphase phenomena in a Eulerian basis. The method is based on the evolution of the signed distance function from interfaces between phases of the flow, and automatically captures complex topological changes of the free surfaces such as breaking and merging. We present an extension to the level set method for modelling the intera...

This paper describes an approach to elastic modelling of human tissue based on the use of 3D solid active models active cubes [2] and a shape description based on the metric tensor in a solid. Active cubes are used because they provide a natural parameterization of the surface and the interior of the given object when deformed to match the object's shape. Using the metric tensor to store the sh...

The Green’s function molecular dynamics method, which enables one to study the elastic response of a three-dimensional solid to an external stress field by taking into consideration only the surface atoms, was implemented as an extension to an open source classical molecular dynamics simulation code LAMMPS. This was done in the style of fixes. The first fix, FixGFC, measures the elastic stiffne...

An efficient method for the simulation of strained heteroepitaxial growth with intermixing using kinetic Monte Carlo is presented. The model used is based on a solid-on-solid bond counting formulation in which elastic effects are incorporated using a ball and spring model. While idealized, this model nevertheless captures many aspects of heteroepitaxial growth, including nucleation, surface dif...

The elastic energy of a multiphase solid is a function of its microstructure. Determining the infimum of the energy of such a solid and characterizing the associated optimal microstructures is an important problem that arises in the modeling of the shape memory effect, microstructure evolution, and optimal design. Mathematically, the problem is to determine the relaxation under fixed phase frac...