Following Castillo et al. 2000 and Cockburn 2003 , a general framework of constructing discontinuous Galerkin DG methods is developed for solving the linear elasticity problem. The numerical traces are determined in view of a discrete stability identity, leading to a class of stable DG methods. A particular method, called the LDG method for linear elasticity, is studied in depth, which can be v...

Abstract. The introduced notion of locally periodic two-scale convergence allows one to average a wider range of microstructures, compared to the periodic one. The compactness theorem for locally periodic two-scale convergence and the characterization of the limit for a sequence bounded in H1(Ω) are proven. The underlying analysis comprises the approximation of functions, with the periodicity w...

We consider a beam whose cross-section is a tubular neighborhood of a simple closed curve γ. We assume that the wall thickness, i.e., the size of the neighborhood, scales with a parameter δε while the length of γ scales with ε. We characterize a thin-walled beam by assuming that δε goes to zero faster than ε. Starting from the three dimensional linear theory of elasticity, by letting ε go to ze...

This paper is concerned with the numerical simulation of the interaction of compressible viscous flow with elastic structures. The flow is described by the compressible Navier-Stokes equations written in the arbitrary Lagrangian-Eulerian (ALE) form. For the elastic deformation we use 2D linear elasticity and nonlinear St. Venant-Kirchhoff and neo-Hookean models. The discretization of both flow ...

A review on mathematical elasticity of quasicrystals is given. In this review, the focus is on various defects of quasicrystals. Dislocation and crack are two classes of typical topological defects, while their existence has great influence on the mechanical behavior of quasicrystals. The analytic and numerical solutions of dislocations and crack in quasicrystals are the core of the static and ...

Realistic elasticity parameters are important for the accurate simulation of deformable objects, e. g. in medical simulations. In this paper, we present an approach for estimating elasticity parameters for isotropic elastic materials using the linear Finite Element Method. Employing the initial undeformed geometry and a measured forcedeformation relation, the method computes the elasticity para...

The real-time capability of ultrasound is it’s major advantage for reconstructive elasticity imaging. In addition to providing important immediate feedback during patient examination, real-time data capture provides an excellent means for retrospective data processing. With retrospective processing, normal axial strain images can be optimized for highest SNR, the accuracy of lateral displacemen...

We are concerned here with the effect of added filler particles on the linear and non-linear rheological properties of viscoelastic systems. Whilst the addition of spherical or near-spherical filler particles will almost always increase the level of both the linear and the non-linear viscometric properties (so leading to increases in pressure drops, etc.), we usually find a decrease in the leve...

The present work is concerned with the analysis of the Discontinuous Galerkin Finite Element Method (DGFEM) for linear • diffusion problems, • elasticity problems,