Longitudinal Pochhammer — Chree Waves in Mild Auxetics and Non-Auxetics

2018 ◽  
Vol 35 (3) ◽  
pp. 327-334 ◽  
Author(s):  
A. V. Ilyashenko ◽  
S. V. Kuznetsov
Keyword(s):  
Poisson’S Ratio ◽  
Wave Speed ◽  
Poisson's Ratio ◽  
Abnormal Behavior ◽  
Axially Symmetric ◽  
Displacement Fields ◽  
Shear Wave Speed ◽  
The Matrix ◽  
The Waves ◽  
Analytical Expressions

ABSTRACTThe exact solutions of Pochhammer — Chree equation for propagating harmonic waves in isotropic elastic cylindrical rods, are analyzed. Spectral analysis of the matrix dispersion equation for the longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of the wave polarization due to variation of Poisson’s ratio for mild auxetics (Poisson’s ratio is greater than -0.5) is analyzed and compared with the non-auxetics. It is observed that polarization of the waves for both considered cases (auxetics and non-auxetics) exhibits abnormal behavior in the vicinity of the bulk shear wave speed.

Polarization of the Longitudinal Pochhammer–Chree Waves

2020 ◽  
Vol 22 (4) ◽  
pp. 1329-1336
Author(s):  
Alla V. Ilyashenko ◽  
Sergey V. Kuznetsov
Keyword(s):  
Wave Speed ◽  
Phase Speed ◽  
Harmonic Waves ◽  
Wave Polarization ◽  
Axially Symmetric ◽  
Displacement Fields ◽  
Shear Wave Speed ◽  
The Matrix ◽  
Circular Frequency ◽  
Analytical Expressions

AbstractThe exact solutions of the linear Pochhammer – Chree equation for propagating harmonic waves in a cylindrical rod, are analyzed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of wave polarization on the free surface due to variation of Poisson’s ratio and circular frequency is analyzed. It is observed that at the phase speed coinciding with the bulk shear wave speed all the components of the displacement field vanish, meaning that no longitudinal axisymmetric Pochhammer – Chree wave can propagate at this phase speed.

Abnormality of the longitudinal Pochhammer–Chree waves in the vicinity of C2 phase speed

2018 ◽  
Vol 24 (23) ◽  
pp. 5642-5649 ◽  
Author(s):  
Sergey V Kuznetsov
Keyword(s):  
Spectral Analysis ◽  
Phase Speed ◽  
Harmonic Waves ◽  
Wave Polarization ◽  
Axially Symmetric ◽  
Displacement Fields ◽  
The Matrix ◽  
Circular Frequency ◽  
Shear Speed ◽  
Analytical Expressions

The exact solutions of the linear Pochhammer–Chree equation for propagating harmonic waves in a cylindrical rod are analyzed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes is performed and analytical expressions for displacement fields are obtained. The variation of wave polarization on the free surface due to the variation of Poisson’s ratio and circular frequency is analyzed. It is observed that at the phase speed coinciding with the bulk shear speed all the components of the displacement field vanish, meaning that no longitudinal axisymmetric Pochhammer–Chree waves can propagate at this phase speed.

Dependence of the Frequency Spectrum of a Circular Disk on Poisson’s Ratio

1957 ◽  
Vol 24 (1) ◽  
pp. 53-54
Author(s):  
R. L. Sharma
Keyword(s):  
Frequency Spectrum ◽  
Poisson’S Ratio ◽  
Circular Disk ◽  
Intermediate Frequency ◽  
Poisson's Ratio ◽  
Axially Symmetric ◽  
Frequency Range ◽  
Flexural Vibrations ◽  
Circular Disks

Abstract The results of computations of frequencies of axially symmetric flexural vibrations of circular disks are given for an intermediate frequency range and for several values of Poisson’s ratio.

Mechanical Properties of Biomimetic Leaf Composite

2016 ◽  
Author(s):  
Hamid Nayeb Hashemi ◽  
Gongdai Liu ◽  
Ashkan Vaziri ◽  
Masoud Olia ◽  
Ranajay Ghosh
Keyword(s):  
Mechanical Properties ◽  
Yield Stress ◽  
Poisson’S Ratio ◽  
Composite Structures ◽  
Volume Fraction ◽  
Fiber Composite ◽  
Poisson's Ratio ◽  
Closed Cell ◽  
Cell Architecture ◽  
The Matrix

In this paper, we mimic the venous morphology of a typical plant leaf into a fiber composite structure where the veins are replaced by stiff fibers and the rest of the leaf is idealized as an elastic perfectly plastic polymeric matrix. The variegated venations found in nature are idealized into three principal fibers — the central mid-fiber corresponding to the mid-rib, straight parallel secondary fibers attached to the mid-fiber representing the secondary veins and then another set of parallel fibers emanating from the secondary fibers mimicking the tertiary veins of a typical leaf. The tertiary fibers do not interconnect the secondary fibers in our present study. We carry out finite element (FE) based computational investigation of the mechanical properties such as Young’s moduli, Poisson’s ratio and yield stress under uniaxial loading of the resultant composite structures and study the effect of different fiber architectures. To this end, we use two broad types of architectures both having similar central main fiber but differing in either having only secondary fibers or additional tertiary fibers. The fiber and matrix volume fractions are kept constant and a comparative parametric study is carried out by varying the inclination of the secondary fibers. We find significant effect of fiber inclination on the overall mechanical properties of the composites with higher fiber angles transitioning the composite increasingly into a matrix-dominated response. We also find that in general, composites with only secondary fibers are stiffer with closed cell architecture of the secondary fibers. The closed cell architecture also arrested the yield stress decrease and Poisson’s ratio increase at higher fiber angles thereby mitigating the transition into the matrix dominated mode. The addition of tertiary fibers also had a pronounced effect in arresting this transition into the matrix dominated mode. However, it was found that indiscriminate addition of tertiary fibers may not provide desired additional stiffness for fixed volume fraction of constituents. In conclusion, introducing a leaf-mimicking topology in fiber architecture can provide significant additional degrees of tunability in design of these composite structures.

Effective Stiffness of Nano and Transformation Composite Ceramics

2007 ◽  
Vol 336-338 ◽  
pp. 2528-2531
Author(s):  
Xiao Bo Lu ◽  
Xie Quan Liu ◽  
Xin Hua Ni ◽  
Shu Qin Zhang
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Effective Stiffness ◽  
Poisson's Ratio ◽  
High Fracture Toughness ◽  
Composite Ceramics ◽  
Average Value ◽  
Volume Average ◽  
The Matrix

The composite ceramics that contains nano-fibers and transformation particles, fabricated through SHS process, is performed with high fracture toughness and high plasticity. The matrix of composite ceramics was mainly composed of fiber eutectics with nano-fibers. The transformation particles were distributed along boundaries of the fiber eutectic structures. First, Mori-Tanaka method was used to predict the stiffness of the fiber eutectic. The fiber eutectic is transverse isotropy and has five independent elastic constants. Then considering random orientation of the fiber eutectic, the Young’s modulus and Poisson’s ratio of the matrix is determined by even strain. The matrix is isotropy. Finely, assuming the transformation particles as spheres distributed in the matrix, the effective stiffness for composite ceramics was computed. When the volume fraction of fibers and particles increase, the Young’s modulus of composite ceramics decrease and are little smaller than the volume average value, the Poisson’s ratio of composite ceramics decrease and are little bigger than the volume average value.

The Effects of Dimension Ratio on the Micropolar Peridynamic Model

2010 ◽  
Author(s):  
Y. Ferhat ◽  
I. Ozkol
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Displacement Field ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Elastic Behavior ◽  
Displacement Fields ◽  
Peridynamic Theory ◽  
Peridynamic Model ◽  
Central Forces

The aim of this study is to investigate the capability of the micropolar peridynamic theory to analyze elastic behavior of plates with various length and width. Since the quantities such as stress and strain are related to displacement field, only the displacement fields of these structures are computed using the micropolar peridynamic model while Poisson’s ratios are kept constant. The results are compared both to the analytical solution of the classical elasticity theory and to the solution of displacement based finite element methods. The software package ANSYS is used for FEM results. To compute the displacement field, a programming code is developed using MATHEMATICA. In the peridynamic theory the constitutive model contains only central forces and can be applied only to the materials having 1/4 Poisson’s ratio. It is the biggest shortcoming of the peridynamic theory. To overcome strict Poisson’s ratio limitation of the peridynamic theory, the micropolar peridynamic theory is proposed. The micropolar peridynamic model allows peridynamic moments, in addition to peridynamic central forces, to interact with the particles inside the material horizon. The introduction of the moments to the theory allows us to deal with the materials having Poisson’s ratio different from 1/4. This modification can be seen as the generalization of the peridynamic theory. Furthermore, the micropolar peridynamic theory can be easily implemented using the finite element methods. This provides easy application of the boundary conditions to the physical model in hand. In this work, by applying the micropolar peridynamic theory, we observed that the displacement fields of the plates are strongly affected by dimensional ratio of the plates. However, it is naturally expected that the micropolar and classical theories should give the same results, at least to a certain extend. This strong dependability on the dimensions of the structure can be a significant shortcoming of the micropolar peridynamic theory.

Free, Transverse Vibrations of a Solid Elastic Mass in an Infinitely Long, Rigid, Circular-Cylindrical Tank

1960 ◽  
Vol 27 (4) ◽  
pp. 663-668 ◽  
Author(s):  
J. H. Baltrukonis
Keyword(s):  
Natural Frequency ◽  
Poisson’S Ratio ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
Poisson's Ratio ◽  
Cylindrical Tank ◽  
Field Equations ◽  
Displacement Fields ◽  
Transverse Vibrations

Making use of the field equations of elasticity, the frequency equation is derived for the free, transverse vibrations of a solid elastic mass contained by an infinitely long, rigid, circular-cylindrical tank. This frequency equation relates the natural circular frequencies and Poisson’s ratio. This relationship is plotted revealing a very interesting steplike variation of the natural frequency with Poisson’s ratio. Displacement fields are plotted for two natural frequencies in each of the first three modes.

Image Contrast of Dislocation Loops Near a Free Surface

1977 ◽  
Vol 35 ◽  
pp. 52-53
Author(s):  
S. M. Ohr
Keyword(s):  
Free Surface ◽  
Dislocation Loop ◽  
Image Contrast ◽  
Stress System ◽  
Shear Stresses ◽  
Dislocation Loops ◽  
Axially Symmetric ◽  
Displacement Fields ◽  
Elastic Fields ◽  
Analytical Expressions

The image contrast of dislocation loops computed in the past has made use of the displacement fields which do not take into account the presence of stress- free foil surfaces. The free surface modifies the elastic fields around a dislocation loop and hence can influence the image contrast observed in the electron microscope. The effect can be significant particularly when the loops lie close to one of the foil surfaces. In general, the elasticity problem of dislocation loops that takes the free surface into account is difficult to handle mathematically. In the present paper, the method of Bastecka1 was extended to obtain explicitly the analytical expressions for the displacement fields around a pure edge circular dislocation loop lying parallel to the foil surface. In this method, the stress fields of an image dislocation loop and another axially symmetric stress system were added in order to eliminate the normal as well as shear stresses at the surface.

scholarly journals Improving the strength and toughness of macroscale double networks by exploiting Poisson’s ratio mismatch

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tsuyoshi Okumura ◽  
Riku Takahashi ◽  
Katsumi Hagita ◽  
Daniel R. King ◽  
Jian Ping Gong
Keyword(s):  
Poisson’S Ratio ◽  
Mechanical Performance ◽  
High Strength ◽  
Soft Materials ◽  
Strengthening Mechanism ◽  
Poisson's Ratio ◽  
Uniaxial Tensile ◽  
The Matrix ◽  
The Difference ◽  
Strength And Toughness

AbstractWe propose a new concept that utilizes the difference in Poisson's ratio between component materials as a strengthening mechanism that increases the effectiveness of the sacrificial bond toughening mechanism in macroscale double-network (Macro-DN) materials. These Macro-DN composites consist of a macroscopic skeleton imbedded within a soft elastic matrix. We varied the Poisson's ratio of the reinforcing skeleton by introducing auxetic or honeycomb functional structures that results in Poisson’s ratio mismatch between the skeleton and matrix. During uniaxial tensile experiments, high strength and toughness were achieved due to two events: (1) multiple internal bond fractures of the skeleton (like sacrificial bonds in classic DN gels) and (2) significant, biaxial deformation of the matrix imposed by the functional skeleton. The Macro-DN composite with auxetic skeleton exhibits up to 4.2 times higher stiffness and 4.4 times higher yield force than the sum of the component materials. The significant improvement in mechanical performance is correlated to the large mismatch in Poisson's ratio between component materials, and the enhancement is especially noticeable in the low-stretch regime. The strengthening mechanism reported here based on Poisson's ratio mismatch can be widely used for soft materials regardless of chemical composition and will improve the mechanical properties of elastomer and hydrogel systems.

Dispersion of Axially Symmetric Waves in Elastic Rods

1962 ◽  
Vol 29 (4) ◽  
pp. 729-734 ◽  
Author(s):  
Morio Onoe ◽  
H. D. McNiven ◽  
R. D. Mindlin
Keyword(s):  
Poisson’S Ratio ◽  
Large Range ◽  
Propagation Constant ◽  
Poisson's Ratio ◽  
Elastic Rods ◽  
Axially Symmetric ◽  
Complex Propagation

The relation between frequency and propagation constant, for axially symmetric waves in an infinitely long, isotropic, circular rod, as given by Pochhammer’s equation, is explored. A spectrum, covering a large range of frequencies, is developed for real, imaginary, and complex propagation constants, and the influence of Poisson’s ratio is described.

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