scholarly journals A Finite-Volume Approach to 1D Nonlinear Elastic Waves: Application to Slow Dynamics

2018 ◽  
Vol 104 (4) ◽  
pp. 561-570 ◽  
Author(s):  
H. Berjamin ◽  
B. Lombard ◽  
G. Chiavassa ◽  
N. Favrie
Keyword(s):  
Finite Volume ◽  
Elastic Waves ◽  
Slow Dynamics ◽  
Finite Volume Approach ◽  
Nonlinear Elastic

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.

scholarly journals A finite volume approach to compressible Large Eddy Simulations

1993 ◽  
Vol 51 (1-2) ◽  
pp. 325-329
Author(s):  
B. J. Geurts ◽  
J. G. M. Kuerten ◽  
A. W. Vreman ◽  
V. Theofilis ◽  
P. J. Zandbergen
Keyword(s):  
Finite Volume ◽  
Large Eddy Simulations ◽  
Large Eddy ◽  
Finite Volume Approach

Moisture Diffusion in Unsaturated Polyester Composites Reinforced with Macambira Natural Fiber: A Finite-Volume Approach

2015 ◽  
Vol 3 ◽  
pp. 89-101
Author(s):  
V.C. de Almeida Cruz ◽  
J.M.P.Q. Delgado ◽  
A.G. Barbosa de Lima ◽  
M.M. Silva Nóbrega ◽  
L.H. de Carvalho ◽  
...  
Keyword(s):  
Water Absorption ◽  
Polymer Composites ◽  
Finite Volume ◽  
Natural Fiber ◽  
Diffusion Theory ◽  
Unsaturated Polyester ◽  
Moisture Diffusion ◽  
Moisture Distribution ◽  
Vegetable Fibers ◽  
Finite Volume Approach

This paper presents a theoretical and experimental study about water absorption in unsaturated polyester polymer composites reinforced with vegetable fibers, with particular reference to macambira fiber. A mathematical modeling based on the liquid diffusion theory has been proposed and numerical procedures using the finite volume technique are presented and discussed. Results of the water absorption kinetic and moisture content distribution for the polymer composites are shown and analyzed. The knowledge of moisture distribution inside the composite is essential for determination of areas that may show delamination problems (moisture induced degradation) due to the weakness of the fiber-matrix interface and consequently reduction in the mechanical properties of the composites.

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