Tensor-linear determinative equations for a nonlinear elastic anisotropic medium

1976 ◽  
Vol 12 (4) ◽  
pp. 375-378
Author(s):  
E. E. Kurchakov
Keyword(s):  
Anisotropic Medium ◽  
Elastic Anisotropic Medium ◽  
Nonlinear Elastic

scholarly journals Stress and Displacement Intensity Factors of Cracks in Anisotropic Media

2020 ◽  
Vol 25 (3) ◽  
pp. 212-218
Author(s):  
S. Kuznetsov ◽  
A. Karakozova
Keyword(s):  
Stress Intensity ◽  
Anisotropic Medium ◽  
Stress Intensity Factors ◽  
Crack Front ◽  
Displacement Discontinuity ◽  
Pseudodifferential Equation ◽  
Intensity Factors ◽  
Elastic Anisotropic Medium ◽  
Arbitrary Anisotropy ◽  
Vector Valued

AbstractA relation connecting stress intensity factors (SIF) with displacement intensity factors (DIF) at the crack front is derived by solving a pseudodifferential equation connecting stress and displacement discontinuity fields for a plane crack in an elastic anisotropic medium with arbitrary anisotropy. It is found that at a particular point on the crack front, the vector valued SIF is uniquely determined by the corresponding DIF evaluated at the same point.

The energy of singular effects in an elastic anisotropic medium

1997 ◽  
Vol 61 (4) ◽  
pp. 653-657
Author(s):  
R.V. Gol'Dshtein ◽  
S.V. Kuznetsov
Keyword(s):  
Anisotropic Medium ◽  
Elastic Anisotropic Medium

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.

The dynamics of combat module with nonlinear elastic support characteristics

2016 ◽  
Vol 0 (14) ◽  
pp. 74-78
Author(s):  
O. I. Khytriak
Keyword(s):  
Elastic Support ◽  
Nonlinear Elastic
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