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Content available remote Polarization of the longitudinal Pochhammer-Chree waves
Ilyashenko A. V., Kuznetsov S. V.
Mechanics and Mechanical Engineering
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2018
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Vol. 22, nr 4
1329--1336
EN
The exact solutions of the linear Pochhammer-Chree equation for propagating harmonicwaves in a cylindrical rod, are analyzed. Spectral analysis of the matrix dispersionequation for longitudinal axially symmetric modes is performed. Analytical expressionsfor displacement fields are obtained. Variation of wave polarization on the free surfacedue to variation of Poisson's ratio and circular frequency is analyzed. It is observed thatat the phase speed coinciding with the bulk shear wave speed all the components of thedisplacement eld vanish, meaning that no longitudinal axisymmetric Pochhammer-Chree wave can propagate at this phase speed.
2
Content available remote Elastic waves in spatially periodic anisotropic media: diffraction by periodic arrays of voids or anisotropic inclusions
Ilyashenko A. V., Kuznetsov S. V.
Mechanics and Mechanical Engineering
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2018
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Vol. 22, nr 1
187--193
EN
A two-scale asymptotic analysis coupled with the spatially periodic fundamental solutions are used for analyzing diffraction of elastic bulk waves propagating in anisotropic media containing periodic inclusions or voids. Explicit equations are derived for the scattering cross sections and velocities of bulk waves propagating in spatially periodic media with arbitrary elastic anisotropy.
3
Content available remote Horizontally polarized shear waves in stratified anisotropic (monoclinic) media
Ilyashenko A. V., Kuznetsov S. V.
Archives of Mechanics
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2018
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Vol. 70, nr 4
305--315
EN
The dispersion relations are derived for the horizontally polarized shear (SH) waves in stratified anisotropic plates with arbitrary elastic anisotropy. Analytical expressions for the vectorial group and ray velocities of SH waves propagating in anisotropic layers with monoclinic symmetry are obtained. Closed form relations between velocities and specific kinetic and strain energy for SH waves are derived and analyzed.
4
Content available remote Cam-clay models in mechanics of granular materials
Ilyashenko A. V., Kuznetsov S. V.
Mechanics and Mechanical Engineering
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2017
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Vol. 21, nr 4
813--821
EN
The mathematical models for granular materials utilizing concept of the critical state, is reviewed. Several extensions of the critical state Modified Cam-Clay (MCC) models are reviewed, including kinematic hardening with bounding surface (BS), the general plasticity (GP) model, extension of the MCC model to include finite strain, and different variants of the pressure hardening rule, including bi-modulus extension, hypoplastic, and the hyperelastic potential extension. The associated flow rules coupled with different hardening equations are considered. In the review the main attention is paid to the case of the infinitesimal strains.
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