Related papers: Rigid elastic solids in relativity
There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…
We show that the equation of motion for a rigid one-dimensional elastic body (i.e. a rod or string whose speed of sound is equal to the speed of light) in a two-dimensional spacetime is simply the wave equation. We then solve this equation…
The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. The equations of motion and stress-energy-momentum tensor for a hyperelastic body are derived from the gauge-invariant action…
Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially…
We derive the equations of motion for relativistic elastic membranes, that is, two-dimensional elastic bodies whose internal energy depends only on their stretching, starting from a variational principle. We show how to obtain conserved…
We study the interaction between gravitational waves and elastic bodies within the framework of relativistic elasticity. Starting from the Lagrangian formulation of relativistic elasticity, we derive the linearized equations governing the…
Conventional descriptions of transverse waves in an elastic solid are limited by an assumption of infinitesimally small gradients of rotation. By assuming a linear response to variations in orientation, we derive an exact description of a…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations in material form ("Lagrangian coordinates"). By applying a basic theorem due to Koch, we prove short-time existence…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…
The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response…
The problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the stochastic version of this problem where the…
We develop a covariant variational framework for relativistic electromagnetic continua (fluids and solid) based on Hamilton's principle formulated directly in the material description. The approach extends the geometric theory of…
We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semi--discrete action…
We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids…
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…
We present an equation of state for elastic matter which allows for purely longitudinal elastic waves in all propagation directions, not just principal directions. The speed of these waves is equal to the speed of light whereas the…
Mechanical and elastic properties of materials are among the most fundamental quantities for many engineering and industrial applications. Here, we present a formulation that is efficient and accurate for calculating the elastic and bending…
A general formalism for obtaining the Lagrangian and Hamiltonian for a one dimensional dissipative system is developed. The formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The…
The aim of this paper is twofold. First, we set up the theory of elastic matter sources within the framework of general relativity in a self-contained manner. The discussion is primarily based on the presentation of Carter and Quintana but…