Application of Implicit Grid-Characteristic Methods for Modeling Wave Processes in Linear Elastic Media

2021 ◽  
pp. 151-160
Author(s):  
Evgeniy Pesnya ◽  
Anton A. Kozhemyachenko ◽  
Alena V. Favorskaya
Keyword(s):  
Elastic Media ◽  
Wave Processes ◽  
Linear Elastic ◽  
Characteristic Methods

Hashin–Shtrikman bounds of periodic linear elastic media with cubic symmetry

2020 ◽  
Vol 25 (5) ◽  
pp. 1182-1198 ◽  
Author(s):  
George Mejak
Keyword(s):  
Variational Principle ◽  
Boundary Value Problem ◽  
Elastic Media ◽  
Macroscopic Strain ◽  
Two Phase ◽  
Cubic Symmetry ◽  
Shear Moduli ◽  
Linear Elastic ◽  
Periodic Linear ◽  
Periodic Composite

Based on the Hashin–Shtrikman variational principle, novel bounds on the effective shear moduli of a two-phase periodic composite are derived. The composite constituents are assumed to be isotropic, while the microstructure is assumed to exhibit cubic symmetry. A solution of the subsidiary boundary value problem is expressed as a double contraction of a fourth-order cubic tensor with the applied macroscopic strain. The bounds for cubic shear moduli are new, while the bounds for the bulk modulus are equal to the classical ones. The new bounds are verified for composites with the cubic, frame, octet and cubic + octet structures. It is shown that they are nearly attained for the cubic, octet and cubic + octet structures.

Numerical simulation of shock wave processes in elastic media and structures. Part II: Application results

2012 ◽  
Vol 48 (5) ◽  
pp. 839-855 ◽  
Author(s):  
M. V. Ayzenberg-Stepanenko ◽  
E. N. Sher ◽  
G. G. Osharovich ◽  
Z. Sh. Yanovitskaya
Keyword(s):  
Numerical Simulation ◽  
Shock Wave ◽  
Elastic Media ◽  
Wave Processes

On the existence of type-6 transonic states in linear elastic media of cubic symmetry

1987 ◽  
Vol 411 (1840) ◽  
pp. 251-263 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Solid ◽  
Mechanics Of Solids ◽  
Elastic Media ◽  
Slowness Surface ◽  
Cubic Symmetry ◽  
Linear Elastic ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

Crucial to the understanding of surface-wave propagation in an anisotropic elastic solid is the notion of transonic states, which are defined by sets of parallel tangents to a centred section of the slowness surface. This study points out the previously unrecognized fact that first transonic states of type 6 (tangency at three distinct points on the outer slowness branch S 1 ) indeed exist and are the rule, rather than the exception, in so-called C 3 cubic media (satisfying the inequalities c 12 + c 44 > c 11 - c 44 > 0); simple numerical analysis is used to predict orientations of slowness sections in which type-6 states occur for 21 of the 25 C 3 cubic media studied previously by Chadwick & Smith (In Mechanics of solids , pp. 47-100 (1982)). Limiting waves and the composite exceptional limiting wave associated with such type-6 states are discussed.

scholarly journals Interaction of highly nonlinear solitary waves with linear elastic media

2011 ◽  
Vol 83 (4) ◽  
Author(s):  
Jinkyu Yang ◽  
Claudio Silvestro ◽  
Devvrath Khatri ◽  
Luigi De Nardo ◽  
Chiara Daraio
Keyword(s):  
Solitary Waves ◽  
Elastic Media ◽  
Linear Elastic ◽  
Highly Nonlinear ◽  
Highly Nonlinear Solitary Waves ◽  
Nonlinear Solitary Waves

The Principle of Asymptotic Proportionality

1990 ◽  
Vol 57 (1) ◽  
pp. 225-231
Author(s):  
H. C. M. Chan
Keyword(s):  
Function Method ◽  
Equilibrium Problems ◽  
Field Variable ◽  
Far Field ◽  
Elastic Media ◽  
Two Dimensional ◽  
Linear Elastic ◽  
Induced Stresses ◽  
Physical Phenomena ◽  
Physical Quantities

The Principle of Asymptotic Proportionality, which is based on the Green’s function method for equilibrium problems, is proposed. Using this principle, the induced far-field variable due to any distribution of applied physical quantities can be approximated. This principle has been verified by considering the induced stresses due to applied tractions and dislocations in two-dimensional linear elastic media, and has been shown to be applicable to other physical phenomena such as electrostatics, gravitation, and electromagnetism.

Numerical simulation of shock-wave processes in elastic media and structures. Part I: Solving method and algorithms

2012 ◽  
Vol 48 (1) ◽  
pp. 76-95 ◽  
Author(s):  
M. V. Ayzenberg-Stepanenko ◽  
G. G. Osharovich ◽  
E. N. Sher ◽  
Z. Sh. Yanovitskaya
Keyword(s):  
Numerical Simulation ◽  
Shock Wave ◽  
Elastic Media ◽  
Wave Processes
Sign in / Sign up

Export Citation Format

Share Document