Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

Nonlinear Elastic Waves in a 1D Layered Composite Material: Some Numerical Results

2011 ◽  
Author(s):  
Igor Andrianov ◽  
Vladislav Danishevs’kyy ◽  
Dieter Weichert ◽  
Heiko Topol ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Composite Material ◽  
Elastic Waves ◽  
Layered Composite ◽  
Numerical Results ◽  
Layered Composite Material ◽  
Nonlinear Elastic

Nonlinear elastic waves in architected soft solids

2017 ◽  
Vol 141 (5) ◽  
pp. 3735-3735
Author(s):  
Bolei Deng ◽  
Jordan R. Raney ◽  
Katia Bertoldi ◽  
Vincent Tournat
Keyword(s):  
Elastic Waves ◽  
Soft Solids ◽  
Nonlinear Elastic

Green function method for nonlinear elastic waves in layered media

2001 ◽  
Vol 90 (8) ◽  
pp. 3762-3770
Author(s):  
A. E. Lobo ◽  
E. N. Tsoy ◽  
C. Martijn de Sterke
Keyword(s):  
Green Function ◽  
Elastic Waves ◽  
Function Method ◽  
Layered Media ◽  
Green Function Method ◽  
Nonlinear Elastic

Propagation of elastic waves in a solid in the case of a nonlinear-elastic model of a continuous medium

1970 ◽  
Vol 6 (2) ◽  
pp. 140-144 ◽  
Author(s):  
G. N. Savin ◽  
A. A. Lukashev ◽  
E. M. Lysko ◽  
S. V. Veremeenko ◽  
S. M. Vozhevskaya
Keyword(s):  
Elastic Waves ◽  
Continuous Medium ◽  
Elastic Model ◽  
Nonlinear Elastic ◽  
Propagation Of Elastic Waves

scholarly journals NONLINEAR ELASTIC WAVES IN A GRANULAR MEDIUM

1992 ◽  
Vol 02 (C1) ◽  
pp. C1-779-C1-782
Author(s):  
A. N. BOGDANOV ◽  
A. T. SKVORTSOV
Keyword(s):  
Elastic Waves ◽  
Granular Medium ◽  
Nonlinear Elastic

scholarly journals Elastic waves in the Hencky-Murnaghan material

2020 ◽  
pp. 108-120
Author(s):  
Марина Юрьевна Соколова ◽  
Юрий Владимирович Астапов
Keyword(s):  
Elastic Constants ◽  
Elastic Waves ◽  
Deformable Body ◽  
Polyamide 6 ◽  
Phase Velocities ◽  
Dynamic Methods ◽  
Nonlinear Elastic ◽  
The Given

Рассмотрены динамические методы идентификации модели нелинейно упругого деформируемого тела. По эффективным фазовым скоростям продольных и поперечных волн, распространяющихся вдоль и поперек оси сжимаемого стержня, возможно определить пять констант упругости второго и третьего порядков, входящих в соотношения модели. В статье получены расчетные формулы и приведен пример определения зависимости фазовых скоростей для полиамида 6. The dynamic methods for selecting models of a nonlinear elastic deformable body are considered. Depending on the model, five elastic constants of the second and third orders, which are available in the relations of the models, can be determined. The calculation formulas and the given example of determining the dependence of phase velocities for polyamide 6 are obtained in the article.

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