Waves in Linear Elastic Media with Microrotations, Part 2: Isotropic Reduced Cosserat Model

2009 ◽  
Vol 99 (2B) ◽  
pp. 1423-1428 ◽  
Author(s):  
E. F. Grekova ◽  
M. A. Kulesh ◽  
G. C. Herman
Keyword(s):  
Elastic Media ◽  
Linear Elastic ◽  
Cosserat Model

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.

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.

Wave-like solutions in Cosserat micropolar elasticity

2021 ◽  
Author(s):  
Christian Boehmer
Keyword(s):  
Wave Velocity ◽  
Elastic Waves ◽  
Nonlinear Partial Differential Equations ◽  
Coupled System ◽  
Material Point ◽  
Micropolar Elasticity ◽  
Linear Elastic ◽  
Cosserat Model ◽  
Material Points ◽  
Rotational Waves

<p>The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only experience microrotations, which is also known as micropolar elasticity. The propagation of elastic waves in such a medium is studied and we find two classes of waves, transversal rotational waves and longitudinal rotational waves, both of which are solutions of the nonlinear partial differential equations. For certain parameter choices, the transversal wave velocity can be greater than the longitudinal wave velocity.  We couple the rotational waves to linear elastic waves to study the behaviour of the coupled system and find wave-like solutions with differing wave speeds. In addition we also consider the so-called Cosserat coupling term. In this setting we seek soliton type solutions assuming small elastic displacements, however, we allow the material points to experience full rotations which are not assumed to be small.</p>

Shock Pressure in Oblique Impact—A Theoretical Analysis

1974 ◽  
Vol 41 (1) ◽  
pp. 124-130 ◽  
Author(s):  
C. A˚ke Persson
Keyword(s):  
Shock Wave ◽  
Pressure Rise ◽  
Impact Angle ◽  
Oblique Impact ◽  
Shock Pressure ◽  
Elastic Media ◽  
Linear Elastic ◽  
Wave Velocities ◽  
Impact Angles ◽  
The Impact

The variation of shock pressure with the angle between the colliding surfaces in an oblique impact between two plane plates is analyzed theoretically. The analysis is carried out for small impact angles and the plate materials are assumed to behave like fluids (Case 1) and linear elastic media (Case 2). In the latter case the two extreme assumptions concerning the friction at the interface, no friction and no sliding, are treated. The results show that the shock pressure increases quadratically with the impact angle (except for some of the no sliding cases, where decreasing pressure can occur) and that the pressure rise is strongly dependent upon the ratio between the impact velocity and the shock wave velocities for the plate materials.

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