Related papers: Two-dimensional defects in amorphous materials

We consider three-dimensional reshaping of thin nemato-elastic sheets containing half-charged defects upon nematic-isotropic transition. Gaussian curvature, that can be evaluated analytically when the nematic texture is known, differs from…

"Curvepole (2,0)-theory" is a deformation of the (2,0)-theory with nonlocal interactions. A "curvepole" is defined as a two-dimensional generalization of a dipole. It is an object of fixed two-dimensional shape whose boundary is a charged…

In this paper, we develop a non-singular continuum theory of point defects based on a second strain gradient elasticity theory, the so-called gradient elasticity of bi-Helmholtz type. Such a generalized continuum theory possesses a weak…

The response of amorphous solids to a mechanical perturbation consists in an elastic and a plastic deformation. The latter is mediated by localized irreversible rearrangements associated with Eshelby-like quadrupolar singularities in the…

We explore models with emergent gravity and metric by means of numerical simulations. A particular type of two-dimensional non-linear sigma-model is regularized and discretized on a quadratic lattice. It is characterized by lattice…

A large family of periodic planar non-linear bimode metamaterials are constructed from rigid bars and pivots. They are affine materials in the sense that their macroscopic deformations are only affine deformations: at large distances any…

In this paper, Neumann cracks in elastic bodies are considered. We establish a rigorous asymptotic expansion for the boundary perturbations of the displacement (and traction) vectors that are due to the presence of a small elastic linear…

We characterise the particlelike kinematics of charge-carrying topological defects in nematic media via a geometric field theory. This differs from the theory of electromagnetism, with which it is often compared, due to the absence of…

Extended defects in crystals, such as dislocations, stacking faults and grain boundaries, play a crucial role in determining a wide variety of materials properties. Extended defects can also lead to novel electronic properties in…

We derive the explicit analytical form for the charge-dipole and dipole-dipole interactions in 2D configuration space. We demonstrate that the reduction of dimensionality can alter the charge-dipole and dipole-dipole interactions in 2D…

Topological defects are an essential part of the structure and dynamics of all liquid crystals, and they are particularly important in experiments and simulations on active liquid crystals. In a recent paper, Vromans and Giomi [Soft Matter,…

Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…

Optical nonlinearity depends on symmetry and symmetries vanish in the presence of defects. Vaccancy defects in centrosymmetric crystals and thin films are a well-known source of even-order optical nonlinearity, e.g. causing second harmonic…

We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…

In this paper, we study a new type of inverse problem on warped product Riemannian manifolds with connected boundary that we name warped balls. Using the symmetry of the geometry, we first define the set of Regge poles as the poles of the…

A continuum description of unstructured meshes in two dimensions, both for planar and curved surface domains, is proposed. The meshes described are those which, in the limit of an increasingly finer mesh (smaller cells), and away from…

The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…

Within a framework of noncommutative geometry, we develop an analogue of (pseudo) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric tensor with a simple geometric…

We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincar\'e dual, equipped with a discrete conformal structure. A lot of theorems of the continuous theory follow…

The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids {\bf 57}, 762 (2009)]. For a class of simple axisymmetric…