The Stiffening Effect of Rigid Elliptical Inclusions on a Power-Law Material

1989 ◽  
Vol 111 (4) ◽  
pp. 368-371 ◽  
Author(s):  
J. M. Duva ◽  
Dirck Storm
Keyword(s):  
Plane Strain ◽  
Constitutive Relation ◽  
Power Law ◽  
Cross Sections ◽  
Particle Shape ◽  
Elliptical Cross ◽  
Plane Strain Deformation ◽  
Self Consistent ◽  
Single Inclusion ◽  
Stiffening Effect

An approximate constitutive relation is derived for plane strain deformation in a power-law viscous matrix reinforced with long rigid inclusions with elliptical cross sections. The analysis is based on the differential self-consistent scheme and numerical calculations estimating the influence of a single inclusion on the material surrounding it. In particular, the effects of particle shape and material nonlinearity are reported.

A Self-Consistent Analysis of the Stiffening Effect of Rigid Inclusions on a Power-Law Material

1984 ◽  
Vol 106 (4) ◽  
pp. 317-321 ◽  
Author(s):  
J. M. Duva
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Constitutive Relation ◽  
Power Law ◽  
Nonlinear Boundary ◽  
Viscous Material ◽  
Spherical Inclusions ◽  
Self Consistent ◽  
Infinite Power ◽  
Stiffening Effect

An approximate constitutive relation is derived for a power-law viscous material stiffened by rigid spherical inclusions using a differential self-consistent analysis. This approach consists of two parts: the formulation of a self-consistent differential equation, and the solution of an associated kernel problem, a nonlinear boundary value problem for an isolated inclusion in an infinite power-law viscous matrix.

scholarly journals The Rules for the Lattice Rotation Accompanying Slip as Derived From a Self-Consistent Model

1999 ◽  
Vol 31 (4) ◽  
pp. 217-230 ◽  
Author(s):  
R. A. Lebensohn ◽  
T. Leffers
Keyword(s):  
Solid Mechanics ◽  
Grain Shape ◽  
Rolling Plane ◽  
Lattice Rotation ◽  
Consistent Model ◽  
Plane Strain Deformation ◽  
Self Consistent ◽  
The One ◽  
Equiaxed Grains ◽  
Very High

The rules for the lattice rotation during rolling (plane strain) deformation of fcc polycrystals are studied with a viscoplastic self-consistent model. Very high values of the ratesensitivity exponent are used in order to establish Sachs-type conditions with large local deviations from the macroscopic strain. The lattice rotation depends on the grain shape. For equiaxed grains the lattice rotation follows the MA rule, which is the one normally used in solid mechanics. For elongated and flat grains the lattice rotation follows a different rule, the PSA rule. In the standard version the model performs a transition from MA to PSA with increasing strain. There is avery clear difference between the textures resulting from the two different rules. MA leads to a copper-type texture, and PSA leads to a brass-type texture.

Numerical Analysis of Branch Mechanical Response to Loading

2019 ◽  
Vol 45 (4) ◽  
Author(s):  
Barbora Vojáčková ◽  
Jan Tippner ◽  
Petr Horáček ◽  
Luděk Praus ◽  
Václav Sebera ◽  
...  
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Mechanical Response ◽  
Mechanical Analysis ◽  
Beam Deflection ◽  
Design System ◽  
Elliptical Cross ◽  
Static Mechanical ◽  
The Difference ◽  
Tree Uprooting

Failure of a tree can be caused by a stem breakage, tree uprooting, or branch failure. While the pulling test is used for assessing the first two cases, there is no device-supported method to assess branch failure. A combination of the optical technique, pulling test, and deflection curve analysis could provide a device-supported tool for this kind of assessment. The aim of the work was to perform a structural analysis of branch response to static mechanical loading. The analyses were carried out by finite element simulations in ANSYS using beam tapered elements of elliptical cross-sections. The numerical analyses were verified by the pulling test combined with a sophisticated optical assessment of deflection evaluation. The Probabilistic Design System was used to find the parameters that influence branch mechanical response to loading considering the use of cantilever beam deflection for stability analysis. The difference in the branch’s deflection between the simulation and the experiment is 0.5% to 26%. The high variability may be explained by the variable modulus of the elasticity of branches. The finite element (FE) sensitivity analysis showed a higher significance of geometry parameters (diameter, length, tapering, elliptical cross-section) than material properties (elastic moduli). The anchorage rotation was found to be significant, implying that this parameter may affect the outcome in mechanical analysis of branch behavior. The branch anchorage can influence the deflection of the whole branch, which should be considered in stability assessment.

Stresses and Deformations of Toroidal Shells of Elliptical Cross Section: With Applications to the Problems of Bending of Curved Tubes and of the Bourdon Gage

1952 ◽  
Vol 19 (1) ◽  
pp. 37-48
Author(s):  
R. A. Clark ◽  
T. I. Gilroy ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Closed Shell ◽  
Open Shell ◽  
Elliptical Cross Section ◽  
Axially Symmetric ◽  
Elliptical Cross ◽  
Two Parameters ◽  
Toroidal Shells

Abstract This paper is concerned with the application of the theory of thin shells to several problems for toroidal shells with elliptical cross section. These problems are as follows: (a) Closed shell subjected to uniform normal wall pressure. (b) Open shell subjected to end bending moments. (c) Combination of the results for the first and second problems in such a way as to obtain results for the stresses and deformations in Bourdon tubes. In all three problems the distribution of stresses is axially symmetric but only in the first problem are the displacements axially symmetric. The magnitude of stresses and deformations for given loads depends in all three problems on the magnitude of the two parameters bc/ah and b/c where b and c are the semiaxes of the elliptical section, a is the distance of the center of the section from the axis of revolution, and h is the thickness of the wall of the shell. For sufficiently small values of bc/ah trigonometric series solutions are obtained. For sufficiently large values of bc/ah asymptotic solutions are obtained. Numerical results are given for various quantities of practical interest as a function of bc/ah for the values 2, 1, 1/2, 1/4 of the semiaxes ratio b/c. It is suggested that the analysis be extended to still smaller values of b/c and to cross sections other than elliptical.

Glaciological Problems Set by the Control of Dangerous Lakes in Cordillera Blanca, Peru. II. Movement of a Covered Glacier Embedded within a Rock Glacier

1977 ◽  
Vol 18 (79) ◽  
pp. 255-274 ◽  
Author(s):  
Louis Lliboutry
Keyword(s):  
Cross Sections ◽  
Rock Glacier ◽  
Measured Velocity ◽  
Elliptical Cross ◽  
Cordillera Blanca ◽  
The Holocene ◽  
Glacier Tongue ◽  
Proglacial Lake

AbstractIn front of Laguna Parón there is a huge moraine which turns through 90° in the middle of the valley and with a narrow covered glacier on the top. It has been studied by electrical exploration, and using the displacements of 43 marked boulders on the glacier. Assuming a uniform balance on the glacier tongue and semi-elliptical cross-sections, it has been possible to estimate this balance and the glacier thickness. A great amount of the measured velocity comes from the creep of the moraine itself, which seems 10 be a kind of rock glacier, probably without interstitial ire. It must have taken all the Holocene to be formed. During its complex history a proglacial lake must have formed at some time, the rupture of which explains the crooked form.

Sign in / Sign up

Export Citation Format

Share Document