Material forces as a simple criterion for the description of crack-turning problems

2006 ◽  
Vol 10 (6) ◽  
pp. 519-526 ◽  
Author(s):  
Stephan Adden ◽  
Marco Merzbacher ◽  
Peter Horst
Keyword(s):  
Simple Criterion ◽  
Material Forces ◽  
Crack Turning

scholarly journals Material parametrization of natural rubber based compound and characterization of crack propagation under consideration of dissipative effects

2021 ◽  
Author(s):  
Dan Pornhagen ◽  
Konrad Schneider ◽  
Markus Stommel
Keyword(s):  
Energy Dissipation ◽  
Crack Propagation ◽  
Natural Rubber ◽  
Experimental Tests ◽  
Material Behavior ◽  
Prony Series ◽  
Material Forces ◽  
Cracking Behavior ◽  
Dissipative Effects

AbstractMost concepts to characterize crack propagation were developed for elastic materials. When applying these methods to elastomers, the question is how the inherent energy dissipation of the material affects the cracking behavior. This contribution presents a numerical analysis of crack growth in natural rubber taking energy dissipation due to the visco-elastic material behavior into account. For this purpose, experimental tests were first carried out under different load conditions to parameterize a Prony series as well as a Bergström–Boyce model with the results. The parameterized Prony series was then used to perform numerical investigations with respect to the cracking behavior. Using the FE-software system ANSYS and the concept of material forces, the influence and proportion of the dissipative components were discussed.

Paper 7: Control of Variable-Discharge Pumps and Dangers of Pipeline Resonance

1966 ◽  
Vol 181 (1) ◽  
pp. 144-174
Author(s):  
B. J. Cooper ◽  
D. Hartland ◽  
R. Lawson ◽  
A. M. Stone ◽  
R. D. Tyler
Keyword(s):  
Power Input ◽  
Small Region ◽  
Significant Loss ◽  
Pump Efficiency ◽  
Positive Slope ◽  
Simple Criterion ◽  
Wide Range ◽  
Resonant Instability ◽  
Organ Pipe ◽  
Computer Studies

The discharge and power input of Deriaz mixed-flow pumps and pump turbines can be controlled over a wide range without significant loss in efficiency by movement of the blades. The attainment of the highest pump efficiency involves a small region of positive slope in the head discharge graph. This paper examines the limitations of designing pumps which do not exhibit positive slope and the problems of governing if a positive-slope region is accepted. It is shown that operation in the positive-slope region can introduce a serious organ-pipe resonant instability in the pipeline. A simple criterion to determine whether or not such oscillations will occur is given. This stability criterion involves the dynamic characteristics of both the pump and the pipeline. Finally, computer studies of a particular Deriaz pump installation are presented. These underline the severity of the situation should resonance develop and show how it can be avoided by the use of an air bottle of appropriate design.

THE ISOPIESTIC METHOD APPLIED TO SORPTION ISOTHERMS

1949 ◽  
Vol 27b (2) ◽  
pp. 87-100 ◽  
Author(s):  
S. Barnartt ◽  
J. B. Ferguson
Keyword(s):  
Carbon Tetrachloride ◽  
Linear Relation ◽  
Sorption Isotherms ◽  
Sorption Process ◽  
The Other ◽  
Isopiestic Method ◽  
Simple Criterion ◽  
Water Vapors ◽  
Linear Sections ◽  
Wide Pressure

The isopiestic method has been applied to the sorption of carbon tetrachloride and water vapors by activated coconut shell charcoals. The isopiestic charges were found to be linearly related over wide pressure ranges. Isotherms formed by plotting the isopiestic charges of two charcoals one against the other consisted of three linear sections for both carbon tetrachloride and water. If the pressure isotherm of one charcoal be known, those of other charcoals may be computed from it by weighing relatively few isopiestic charges. Errors inherent in the measurement of equilibrium pressures, as well as those caused by the drift of the pressure isotherms towards higher sorption capacities at a given pressure, are eliminated in the isopiestic method of comparing charcoals. The linear relation between the isopiestic charges affords a simple criterion of rejection for equations proposed to fit the pressure isotherms. It also throws into relief the structural regularities in activated charcoals. The existence of discontinuities m the sorption process, reported by previous experimenters, is supported by the isopiestic data.

ON MAGNETIC SELF-COLLIMATION OF RELATIVISTIC JETS

2010 ◽  
Vol 19 (06) ◽  
pp. 689-694
Author(s):  
N. GLOBUS ◽  
V. CAYATTE ◽  
C. SAUTY
Keyword(s):  
Black Hole ◽  
Total Energy ◽  
Ideal Fluid ◽  
Polar Axis ◽  
Kerr Metric ◽  
Relativistic Jets ◽  
Simple Criterion ◽  
General Relativistic ◽  
Time Splitting ◽  
Relativistic Magnetohydrodynamics

We present a semi-analytical model using the equations of general relativistic magnetohydrodynamics (GRMHD) for jets emitted by a rotating black hole. We assume steady axisymmetric outflows of a relativistic ideal fluid in Kerr metrics. We express the conservation equations in the frame of the FIDucial Observer (FIDO or ZAMO) using a 3+1 space–time splitting. Calculating the total energy variation between a non-polar field line and the polar axis, we extend to the Kerr metric the simple criterion for the magnetic collimation of jets obtained for a nonrotating black hole by Meliani et al.10 We show that the black role rotation induced a more efficient magnetic collimation of the jet.

scholarly journals On the Homogenization of Material Forces

PAMM ◽  
2011 ◽  
Vol 11 (1) ◽  
pp. 549-550
Author(s):  
Sarah Ricker ◽  
Julia Mergheim ◽  
Paul Steinmann ◽  
Ralf Müller
Keyword(s):  
Material Forces

The Hilbert series of the irreducible quotient of the polynomial representation of the rational Cherednik algebra of type An−1 in characteristic p for p|n − 1

2021 ◽  
pp. 2250191
Author(s):  
Merrick Cai ◽  
Daniil Kalinov
Keyword(s):  
Hilbert Series ◽  
Positive Characteristic ◽  
Closed Field ◽  
Simple Criterion ◽  
Characteristic P ◽  
Polynomial Representation ◽  
Cherednik Algebra ◽  
Rational Cherednik Algebra ◽  
Polynomial Formula ◽  
Field Of Positive Characteristic

In this paper, we study the irreducible quotient [Formula: see text] of the polynomial representation of the rational Cherednik algebra [Formula: see text] of type [Formula: see text] over an algebraically closed field of positive characteristic [Formula: see text] where [Formula: see text]. In the [Formula: see text] case, for all [Formula: see text] we give a complete description of the polynomials in the maximal proper graded submodule [Formula: see text], the kernel of the contravariant form [Formula: see text], and subsequently find the Hilbert series of the irreducible quotient [Formula: see text]. In the [Formula: see text] case, we give a complete description of the polynomials in [Formula: see text] when the characteristic [Formula: see text] and [Formula: see text] is transcendental over [Formula: see text], and compute the Hilbert series of the irreducible quotient [Formula: see text]. In doing so, we prove a conjecture due to Etingof and Rains completely for [Formula: see text], and also for any [Formula: see text] and [Formula: see text]. Furthermore, for [Formula: see text], we prove a simple criterion to determine whether a given polynomial [Formula: see text] lies in [Formula: see text] for all [Formula: see text] with [Formula: see text] and [Formula: see text] fixed.

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