Nonlinear Waves in Solid Continua with Finite Deformation

Finite Element Approximations of Nonlinear Elastic Waves

In this paper we study finite element methods for a class of problems of nonlinear elastodynamics. We discretize the equations in space using Galerkin methods. For the temporal discretization, the construction of our schemes is based on rational approximations of cosx and ex . We analyze semidiscrete as well as secondand fourth-order accurate in time fully discrete methods for the approximation...

Nonlinear Bulk Elastic Waves in Layered Solid Wave Guides

During the last decade we have performed theoretical investigations and successful experimental research demonstrating the existence and main properties of bulk strain solitary waves in nonlinearly elastic solid wave guides. Following the topic we present preliminary results on strain soliton propagation in layered wave guides made of PMMA. The obvious physical relevance of data on strain solit...

On Nonlinear Water Waves in a Channel

Resonant interactions of nonlinear water waves in a finite basin.

We study exact four-wave resonances among gravity water waves in a square box with periodic boundary conditions. We show that these resonant quartets are linked with each other by shared Fourier modes in such a way that they form independent clusters. These clusters can be formed by two types of quartets: (1) Angle resonances which cannot directly cascade energy but which can redistribute it am...

Multiscale Evaluation of the Nonlinear Elastic Properties of Carbon Nanotubes Under Finite Deformation

This paper deals with the calculation of the elastic properties for single-walled carbon nanotubes (SWCNTs) under axial deformation and hydrostatic pressure using the atomistic-based continuum approach and the deformation mapping technique. A hyperelastic model based on the higher-order Cauchy-Born (HCB) rule being applicable at finite strains and accounting for the chirality and material nonli...