Calibration of a Nonlinear Elastic Composite With Goal-Oriented Error Control

2005 ◽  
Vol 3 (3) ◽  
pp. 363-378 ◽  
Author(s):  
Hakan Johansson ◽  
Kenneth Runesson ◽  
Fredrik Larsson
Keyword(s):  
Error Control ◽  
Elastic Composite ◽  
Nonlinear Elastic ◽  
Nonlinear Elastic Composite

On determining the mechanical properties of nonlinear-elastic composite materials

1996 ◽  
Vol 37 (6) ◽  
pp. 917-925
Author(s):  
I. G. Teregulov ◽  
Yu. I. Butenko ◽  
R. A. Kayumov ◽  
D. Kh. Safiullin ◽  
K. P. Alekseev
Keyword(s):  
Mechanical Properties ◽  
Composite Materials ◽  
Elastic Composite ◽  
Nonlinear Elastic ◽  
Nonlinear Elastic Composite

Evaluation of hybrid error control systems

1984 ◽  
Vol 131 (2) ◽  
pp. 183
Author(s):  
D. Drajić ◽  
B. Vučetić
Keyword(s):  
Control Systems ◽  
Error Control

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.

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