相关论文: Relaxation theorems in nonlinear elasticity

We propose a method for deriving equivalent one-dimensional models for slender non-linear structures. The approach is designed to be broadly applicable, and can handle in principle finite strains, finite rotations, arbitrary cross-sections…

In this paper we present a dimensional reduction to obtain a one-dimensional model to analyze localized necking or bulging in a residually stressed circular cylindrical solid. The nonlinear theory of elasticity is first specialized to…

In this article we consider the linear elasticity problem in an axisymmetric three dimensional domain, with data which are axisymmetric and have zero angular component. The weak formulation of the the three dimensional problem reduces to a…

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…

If a contact of two purely elastic bodies with no sliding (infinite coefficient of friction) is subjected to superimposed oscillations in the normal and tangential directions, then a specific damping appears, that is not dependent on…

In this paper, we study an elastic bilayer plate composed of a nematic liquid crystal elastomer in the top layer and a nonlinearly elastic material in the bottom layer. While the bottom layer is assumed to be stress-free in the flat…

Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…

The classical flexure problem of non-linear incompressible elasticity is revisited for elastic materials whose mechanical response is different in tension and compression---the so-called bimodular materials. The flexure problem is chosen to…

In this paper we apply both the procedure of dimension reduction and the incorporation of structured deformations to a three-dimensional continuum in the form of a thinning domain. We apply the two processes one after the other, exchanging…

The nonlinear dynamics of an elastic filament that is forced to rotate at its base is studied by hydrodynamic simulation techniques; coupling between stretch, bend, twist elasticity and thermal fluctuations is included. The…

We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic energy and write the equilibrium problem as a minimization problem. Applying the direct methods of the calculus of variations we show the existence of…

The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe, including the accelerated expansion. The analogy is manifested…

The relaxation limit in critical Besov spaces for the multidimensional compressible Euler equations is considered. As the first step of this justification, the uniform (global) classical solutions to the Cauchy problem with initial data…

In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…

We study the problem of the motion of the free surface of a liquid. We prove existence and stability for the linearized equations.

Nontrivial infinitesimal bendings for a class of two-dimensional surfaces are constructed. The surfaces considered here are orientable; compact; with boundary; have positive curvature everywhere except at finitely many planar points; and…

The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…

An initial-boundary value problem for the multidimensional type III thermoelaticity for a nonsimple material with a center of symmetry is considered. In the linear case, the well-posedness with and without Kelvin-Voigt and/or frictional…

Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…

We discuss the structure and main features of the nonlinear evolution equation proposed by this author as the fundamental dynamical law within the framework of Quantum Thermodynamics. The nonlinear equation generates a dynamical group…