Stability of homogeneous deformations of an incompressible elastic body under dead-load surface tractions

1987 ◽  
Vol 17 (3) ◽  
pp. 223-248 ◽  
Author(s):  
Yi-Chao Chen
Keyword(s):  
Elastic Body ◽  
Dead Load ◽  
Load Surface ◽  
Incompressible Elastic Body

Pairwise Deformations of an Incompressible Elastic Body under Dead-Load Tractions

2003 ◽  
Vol 73 (1-3) ◽  
pp. 237-249 ◽  
Author(s):  
Pietro D'Ambrosio ◽  
Domenico De Tommasi ◽  
Pilade Foti ◽  
Mario Daniele Piccioni
Keyword(s):  
Elastic Body ◽  
Dead Load ◽  
Incompressible Elastic Body

Stability and possible bifurcations for a Gent-Thomas elastic parallelepiped subject to dead-load surface tractions

2018 ◽  
Vol 207 ◽  
pp. 50-58
Author(s):  
Pilade Foti ◽  
Aguinaldo Fraddosio ◽  
Salvatore Marzano ◽  
Mario Daniele Piccioni
Keyword(s):  
Dead Load ◽  
Load Surface

Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions

1983 ◽  
Vol 94 (2) ◽  
pp. 315-339 ◽  
Author(s):  
J. M. Ball ◽  
D. G. Schaeffer
Keyword(s):  
Elastic Body ◽  
Deformation Gradient ◽  
The Body ◽  
Reference Configuration ◽  
Equilibrium Solutions ◽  
Dead Load ◽  
Homogeneous Equilibrium ◽  
Equilibrium Configurations ◽  
The Stability ◽  
Static Criterion

In this paper we consider the equilibrium configurations of a homogeneous, incompressible, isotropic elastic body subjected to a uniform dead load surface traction of magnitude T whose direction is normal to the surface of the body in the reference configuration, and to no other forces. We concentrate on homogeneous equilibrium solutions, that is those for which the deformation gradient F is constant, and we study their bifurcations and stability (with respect to an appropriate static criterion) as T varies. Since it turns out that the equations for homogeneous equilibrium solutions, and the stability properties that we consider of these solutions, are independent of the shape of the body in the reference configuration, we can suppose if desired that this shape is a cube. (See Fig. 1.1.)

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

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