相关论文: An elementary proof of the Vigdergauz equations fo…
Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic material and the material symmetries of the effective, macroscopic…
This article is a description of elasticity theory for readers with mathematical background. The first sections are an abridgment of parts of the book by Marsden and Hughes, including a compact identification of the equations of motion as…
In this paper we prove a recursive characterisation of generic rigidity for frameworks periodic with respect to a partially variable lattice. We follow the approach of modelling periodic frameworks as frameworks on a torus and use the…
Many biological and engineering materials have nonperiodic microstructures for which classical periodic homogenization results do not apply. Certain nonperiodic microstructures may be approximated by locally periodic microstructures for…
The embedding theorem arises in several problems from analysis and geometry. The purpose of this paper is to provide a deeper understanding of analysis and geometry with a particular focus on embedding theorems on spaces of homogeneous type…
The introduced notion of locally-periodic two-scale convergence allows to average a wider range of microstructures, compared to the periodic one. The compactness theorem for the locally-periodic two-scale convergence and the…
We consider periodic homogenization of nonlinearly elastic composite materials. Under suitable assumptions on the stored energy function (frame indifference; minimality, non-degeneracy and smoothness at identity; $p\geq d$-growth from…
We consider the system of $N$ ($\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$, $\nu\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the full…
We present a novel derivation of the elastic theory of shells. We use the language of Geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools…
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…
Our previous study [1] has demonstrated that the gauge theory is a proper framework for characterizing the local temporal and spatial interactions in inhomogeneous elastic media. However, in that study temporal interactions were interpreted…
We consider the system of $N$ ($\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$, $\nu\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the full…
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…
The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions…
We elucidate consistency of the so-called corner equations which are elementary building blocks of Euler-Lagrange equations for two-dimensional pluri-Lagrangian problems. We show that their consistency can be derived from the existence of…
We consider a periodic lattice structure in $d=2$ or $3$ dimensions with unit cell comprising $Z$ thin elastic members emanating from a similarly situated central node. A general theoretical approach provides an algebraic formula for the…
The classical Szeg\H{o}-Verblunsky theorem relates integrability of the logarithm of the absolutely continuous part of a probability measure on the circle to square summability of the sequence of recurrence coefficients for the orthogonal…
By using tensor analysis, we find a connection between normed algebras and the parallelizability of the spheres S$^1$, S$^3$ and S$^7.$ In this process, we discovered the analogue of Hurwitz theorem for curved spaces and a geometrical…
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…
We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…