Two examples in nonlinear elasticity

1978 ◽  
pp. 41-48 ◽  
Author(s):  
J. M. Ball ◽  
R. J. Knops ◽  
J. E. Marsden
Keyword(s):  
Nonlinear Elasticity

Variant of Nonlinear Elasticity Relations

2019 ◽  
Vol 54 (8) ◽  
pp. 1182-1188
Author(s):  
A. A. Markin ◽  
M. Yu. Sokolova
Keyword(s):  
Nonlinear Elasticity

Exploration of trabecular bone nonlinear elasticity using time of flight modulation

2007 ◽  
Author(s):  
Guillaume Renaud ◽  
Samuel Callé ◽  
Jean-Pierre Remenieras ◽  
Marielle Defontaine
Keyword(s):  
Trabecular Bone ◽  
Nonlinear Elasticity ◽  
Time Of Flight

scholarly journals Vibrations of Nonlinear Elastic Structure Excited by Compressible Flow

2021 ◽  
Vol 11 (11) ◽  
pp. 4748
Author(s):  
Monika Balázsová ◽  
Miloslav Feistauer ◽  
Jaromír Horáček ◽  
Adam Kosík
Keyword(s):  
Compressible Flow ◽  
Nonlinear Elasticity ◽  
Vocal Tract ◽  
Stokes Equations ◽  
Vocal Folds ◽  
Nonlinear Material ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Reliable Solution

This study deals with the development of an accurate, efficient and robust method for the numerical solution of the interaction of compressible flow and nonlinear dynamic elasticity. This problem requires the reliable solution of flow in time-dependent domains and the solution of deformations of elastic bodies formed by several materials with complicated geometry depending on time. In this paper, the fluid–structure interaction (FSI) problem is solved numerically by the space-time discontinuous Galerkin method (STDGM). In the case of compressible flow, we use the compressible Navier–Stokes equations formulated by the arbitrary Lagrangian–Eulerian (ALE) method. The elasticity problem uses the non-stationary formulation of the dynamic system using the St. Venant–Kirchhoff and neo-Hookean models. The STDGM for the nonlinear elasticity is tested on the Hron–Turek benchmark. The main novelty of the study is the numerical simulation of the nonlinear vocal fold vibrations excited by the compressible airflow coming from the trachea to the simplified model of the vocal tract. The computations show that the nonlinear elasticity model of the vocal folds is needed in order to obtain substantially higher accuracy of the computed vocal folds deformation than for the linear elasticity model. Moreover, the numerical simulations showed that the differences between the two considered nonlinear material models are very small.

A field theory approach to stability of radial equilibria in nonlinear elasticity

1986 ◽  
Vol 99 (3) ◽  
pp. 589-604 ◽  
Author(s):  
J. Sivaloganathan
Keyword(s):  
Field Theory ◽  
Calculus Of Variations ◽  
Nonlinear Elasticity ◽  
Isotropic Material ◽  
Theory Approach ◽  
Radial Solutions ◽  
Equilibrium Equations ◽  
The Stability ◽  
State Of Tension

In this paper we study the stability of a class of singular radial solutions to the equilibrium equations of nonlinear elasticity, in which a hole forms at the centre of a ball of isotropic material held in a state of tension under prescribed boundary displacements. The existence of such cavitating solutions has been shown by Ball[1], Stuart [11] and Sivaloganathan[10]. Our methods involve elements of the field theory of the calculus of variations and provide a new unified interpretation of the phenomenon of cavitation.

Sign in / Sign up

Export Citation Format

Share Document