Determination of Effective Moduli

2007 ◽  
pp. 154-195 ◽  
Keyword(s):  
Effective Moduli

A Generalized Self-Consistent Mechanics Method for Solids Containing Elliptical Inclusions

1995 ◽  
Vol 62 (3) ◽  
pp. 566-572 ◽  
Author(s):  
Y. Huang ◽  
K. X. Hu
Keyword(s):  
Aspect Ratio ◽  
Current Approach ◽  
Effective Moduli ◽  
Shear Moduli ◽  
Aspect Ratios ◽  
Isotropic Distribution ◽  
Energy Equivalence ◽  
Self Consistent ◽  
Consistent Method

The determination of the effective moduli for a material containing elliptical inclusions is the objective of this paper. This is done by incorporating an inclusion/matrix/composite model into a general energy equivalence framework. Through the evaluation of the average strain in each individual inclusion, the current approach can handle the inclusion’s orientation dependency in a straightforward manner. The case of an in-plane isotropic distribution of elliptical inclusions is addressed in detail. For the case of reinforcements, or hard inclusions, the effect of the inclusion aspect ratio on in-plane effective moduli is small if the aspect ratio is larger than 0.5. For aspect ratios less than 0.3, the effective moduli increase dramatically, which implies that flat reinforcements are much more effective than traditional cylindrical reinforcements. It is also established that the generalized self-consistent method predicts a stronger dependence of effective moduli on the inclusion aspect ratio than does the Mori-Tanaka method, especially for shear moduli.

Computational Homogenization in Peristatics of Periodic Structure Composites

2018 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Composite Material ◽  
Periodic Structure ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Computational Homogenization ◽  
Effective Moduli ◽  
One Dimensional ◽  
Representative Unit Cell ◽  
Mechanical Influence

A composite material (CM) of periodic structure with the peristatic properties of constituents (see Silling, J. Mech. Phys. Solids 2000; 48:175–209) is analyzed by a generalization of the classical locally elastic computational homogenization to its peristatic counterpart. One introduces new volumetric periodic boundary conditions (PBC) at the interaction boundary of a representative unit cell (UC). A generalization of the Hill’s equality to peristatic composites is proved. The general results establishing the links between the effective moduli and the corresponding mechanical influence functions are obtained. The discretization of the equilibrium equation acts as a macro-to-micro transition of the deformation-driven type, where the overall deformation is controlled. Determination of the microstructural displacements allows one to estimate the peristatic traction at the geometrical UC’s boundary which is exploited for estimation of the macroscopic stresses and the effective moduli. One demonstrates computationally, through one-dimensional examples, the approach proposed.

Computational homogenization in linear elasticity of peristatic periodic structure composites

2018 ◽  
Vol 24 (8) ◽  
pp. 2497-2525 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Composite Material ◽  
Periodic Structure ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Computational Homogenization ◽  
Effective Moduli ◽  
One Dimensional ◽  
Representative Unit Cell ◽  
Mechanical Influence

A composite material (CM) of periodic structure with the peristatic properties of constituents, as proposed by Silling, is analyzed by a generalization of the classical locally elastic computational homogenization to its peristatic counterpart. New volumetric periodic boundary conditions (PBCs) are introduced at the interaction boundary of a representative unit cell (UC). A generalization of the Hill’s equality to peristatic composites is proved. The general results establishing the links between the effective moduli and the corresponding mechanical influence functions are obtained. The discretization of the equilibrium equation acts as a macro-to-micro transition of the deformation-driven type, where the overall deformation is controlled. Determination of the microstructural displacements allows one to estimate the peristatic traction at the geometrical UC’s boundary, which is exploited for estimation of the macroscopic stresses and the effective moduli. The proposed approach is demonstrated computationally through one-dimensional examples.

Galactic orbits of stars

1966 ◽  
Vol 25 ◽  
pp. 93-97
Author(s):  
Richard Woolley
Keyword(s):  
Globular Cluster ◽  
Potential Field ◽  
High Velocity ◽  
Velocity Vector ◽  
Variable Stars ◽  
The Sun ◽  
Proper Motions ◽  
Rr Lyrae ◽  
The Galaxy

It is now possible to determine proper motions of high-velocity objects in such a way as to obtain with some accuracy the velocity vector relevant to the Sun. If a potential field of the Galaxy is assumed, one can compute an actual orbit. A determination of the velocity of the globular clusterωCentauri has recently been completed at Greenwich, and it is found that the orbit is strongly retrograde in the Galaxy. Similar calculations may be made, though with less certainty, in the case of RR Lyrae variable stars.

Distance to SN 1987A and the LMC

1999 ◽  
Vol 190 ◽  
pp. 549-554
Author(s):  
Nino Panagia
Keyword(s):  
Angular Size ◽  
Large Magellanic Cloud ◽  
Magellanic Cloud ◽  
Light Curves ◽  
Distance Modulus ◽  
Absolute Size ◽  
Sn 1987A

Using the new reductions of the IUE light curves by Sonneborn et al. (1997) and an extensive set of HST images of SN 1987A we have repeated and improved Panagia et al. (1991) analysis to obtain a better determination of the distance to the supernova. In this way we have derived an absolute size of the ringRabs= (6.23 ± 0.08) x 1017cm and an angular sizeR″ = 808 ± 17 mas, which give a distance to the supernovad(SN1987A) = 51.4 ± 1.2 kpc and a distance modulusm–M(SN1987A) = 18.55 ± 0.05. Allowing for a displacement of SN 1987A position relative to the LMC center, the distance to the barycenter of the Large Magellanic Cloud is also estimated to bed(LMC) = 52.0±1.3 kpc, which corresponds to a distance modulus ofm–M(LMC) = 18.58±0.05.

International determination of the total motion of the pole

1961 ◽  
Vol 13 ◽  
pp. 29-41
Author(s):  
Wm. Markowitz
Keyword(s):  
Secular Motion ◽  
The Future

A symposium on the future of the International Latitude Service (I. L. S.) is to be held in Helsinki in July 1960. My report for the symposium consists of two parts. Part I, denoded (Mk I) was published [1] earlier in 1960 under the title “Latitude and Longitude, and the Secular Motion of the Pole”. Part II is the present paper, denoded (Mk II).

Time and Latitude in South Africa

1972 ◽  
Vol 1 ◽  
pp. 27-38
Author(s):  
J. Hers
Keyword(s):  
South Africa ◽  
Cape Town ◽  
Astronomical Observations ◽  
Royal Observatory ◽  
The Republic ◽  
Astronomical Determination ◽  
Limited Accuracy ◽  
Better Than

In South Africa the modern outlook towards time may be said to have started in 1948. Both the two major observatories, The Royal Observatory in Cape Town and the Union Observatory (now known as the Republic Observatory) in Johannesburg had, of course, been involved in the astronomical determination of time almost from their inception, and the Johannesburg Observatory has been responsible for the official time of South Africa since 1908. However the pendulum clocks then in use could not be relied on to provide an accuracy better than about 1/10 second, which was of the same order as that of the astronomical observations. It is doubtful if much use was made of even this limited accuracy outside the two observatories, and although there may – occasionally have been a demand for more accurate time, it was certainly not voiced.

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