相关论文: Auxetic deformations and elliptic curves

We establish existence, uniqueness and optimal regularity results for very weak solutions to certain nonlinear elliptic boundary value problems. We introduce structural asymptotic assumptions of Uhlenbeck type on the nonlinearity, which are…

New results are presented for the degeneracy condition of elastic waves in anisotropic materials. The existence of acoustic axes involves a traceless symmetric third order tensor that must vanish identically. It is shown that all previous…

We provide a framework for using elliptic curves with complex multiplication to determine the primality or compositeness of integers that lie in special sequences, in deterministic quasi-quadratic time. We use this to find large primes,…

This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…

In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…

Two classes of non-linear elastic materials are derived via two-dimensional homogenization. These materials are equivalent to a periodic grid of axially-deformable and axially-preloaded structural elements, subject to incremental…

We investigate the behaviour of vertices and inflexions on 1-parameter families of curves on smooth surfaces in the 3-space, which include a singular member. In particular, we discuss the context where the curves evolve as sections of a…

We study the problem of a cholesteric liquid crystal confined to an elliptical channel. The system is geometrically frustrated because the cholesteric prefers to adopt a uniform rate of twist deformation, but the elliptical domain precludes…

Auxetic materials are of great engineering interest not only because of their fascinating negative Poisson's ratio, but also due to their increased toughness and indentation resistance. These materials are typically synthesized polyester…

A theory of flexibility and rigidity is developed for general infinite bar-joint frameworks (G,p). Determinations of nondeformability through vanishing flexibility are obtained as well as sufficient conditions for deformability. Forms of…

Additively manufactured auxetic structures offer desirable qualities like lightweight, good energy absorption, excellent indentation resistance, high shear stiffness and fracture toughness among others. A wide range of materials from…

This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…

In this paper we consider the isoptic curves on the 2-dimensional geometries of constant curvature $\bE^2,~\bH^2,~\cE^2$. The topic is widely investigated in the Euclidean plane $\bE^2$ see for example \cite{CMM91} and \cite{Wi} and the…

Auxetic metamaterials are commonly thought to exhibit favorable mechanical properties, notably high energy absorption. Here we investigate disordered metamaterials obtained from random beam networks by optimizing simultaneously auxeticity…

We examine a fundamental material property called Poisson's ratio, which establishes the relationship for the relative deformation of a physical system in orthogonal directions. Architects and engineers have designed advanced systems using…

Quasicrystals are aperiodically ordered solids that exhibit long-range order without translational periodicity, bridging the gap between crystalline and amorphous materials. Due to their lack of translational periodicity, information on…

We develop a rigidity theory for bar-joint frameworks in Euclidean $d$-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class.…

We prove weighted anisotropic analytic estimates for solutions of second order elliptic boundary value problems in polyhedra. The weighted analytic classes which we use are the same as those introduced by Guo in 1993 in view of establishing…

Auxetic materials, or negative-Poisson's-ratio materials, are important technologically and fascinating theoretically. When loaded by external stresses, their internal strains are governed by correlated motion of internal structural degrees…

The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These…