scholarly journals Mathematical and numerical model for nonlinear viscoplasticity

2011 ◽  
Vol 369 (1947) ◽  
pp. 2864-2880 ◽  
Author(s):  
N. Favrie ◽  
S. Gavrilyuk
Keyword(s):  
Numerical Model ◽  
Specific Energy ◽  
Macroscopic Model ◽  
Material Behaviour ◽  
Plastic Deformations ◽  
Numerical Examples ◽  
Von Mises ◽  
Physical Phenomena ◽  
Deviatoric Part ◽  
Special Case

A macroscopic model describing elastic–plastic solids is derived in a special case of the internal specific energy taken in separable form: it is the sum of a hydrodynamic part depending only on the density and entropy, and a shear part depending on other invariants of the Finger tensor. In particular, the relaxation terms are constructed compatible with the von Mises yield criteria. In addition, Maxwell-type material behaviour is shown up: the deviatoric part of the stress tensor decays during plastic deformations. Numerical examples show the ability of this model to deal with real physical phenomena.

A Generalized von Mises Criterion for Yield and Fracture

1980 ◽  
Vol 47 (2) ◽  
pp. 297-300 ◽  
Author(s):  
W. H. Yang
Keyword(s):  
Bauschinger Effect ◽  
Hydrostatic Stress ◽  
Fracture Criteria ◽  
Deformation History ◽  
Von Mises Criterion ◽  
Effect On Yield ◽  
Von Mises ◽  
New Criterion ◽  
Physical Phenomena ◽  
Special Case

Yield and fracture criteria for real materials are to a varying degree affected by a state of hydrostatic stress. Some materials, after certain deformation history, exhibit different yield point when the direction of the stress is reversed, a behavior known as the Bauschinger effect. These physical phenomena are not represented by the von Mises criterion. Based on a convexity theorem of matrices, a generalization of the von Mises criterion is presented. The new criterion satisfies the convexity requirement of plasticity theory and, with two scalar functions of deformation history α and β, produces a class of hardening behavior. The current values of α and β account for the effect of hydrostatic stress and an aspect of the Bauschinger effect on yield and fracture. The generalized criterion reduces to the form of the von Mises criterion as a special case.

The mathematical modelling of corrosion in hot dip galvanized steel reinforced concrete

2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Equation System ◽  
Galvanized Steel ◽  
Steel Reinforced Concrete ◽  
Numeric Model ◽  
Physical And Mathematical Models ◽  
Physical Phenomena ◽  
The Mathematical Model

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.

Experimental and Numerical Investigation Into the Effects of Initial Conditions on a Three Degree of Freedom Capsize Model

2006 ◽  
Vol 50 (01) ◽  
pp. 63-84
Author(s):  
Young-Woo Lee ◽  
Leigh McCue ◽  
Michael Obar ◽  
Armin Troesch
Keyword(s):  
Numerical Model ◽  
Numerical Investigation ◽  
Initial Conditions ◽  
Degree Of Freedom ◽  
Transient Effects ◽  
Ultimate State ◽  
Extreme Behavior ◽  
Three Degree Of Freedom ◽  
Physical Phenomena ◽  
Ship Capsizing

The dynamics and hydrodynamics of ship capsizing include strong nonlinearities, transient effects, and physical phenomena that have not been fully identified or studied. This paper presents a study of some of the various mechanisms associated with this extreme behavior. A quasi-nonlinear three degree of freedom numerical model is employed to examine the effects of initial conditions on the ultimate state of a box barge model. The numerical results are then used to provide structure and understanding to otherwise seemingly inconsistent and ambiguous experiments.

Acceleration Analysis of Platform-Type Manipulators

1996 ◽  
Author(s):  
Maher G. Mohamed
Keyword(s):  
Stewart Platform ◽  
Algebraic Manipulation ◽  
Analysis Procedure ◽  
Compact Form ◽  
Numerical Examples ◽  
Acceleration Field ◽  
Center Point ◽  
Planar Manipulators ◽  
Acceleration Analysis ◽  
Special Case

Abstract The screw algebra is used to efficiently derive expressions in compact form for both the angular accelerations of the moving links and the linear accelerations of points on the links of platform-type manipulators. The analysis employs the property that the acceleration state of the manipulator platform can be determined by considering the acceleration states of the links of only one — any one — of the manipulator legs. The obtained expressions provide an ease in symbolic and algebraic manipulation. The analysis is then extended to specify the acceleration center point of ithe nstantaneous motion of the manipulator platform. The acceleration center point is then used in expressing the distribution of the acceleration field of the platform instant motion which is important in manipulator synthesis. The special case of planar manipulators is studied and simpler expressions are derived. Numerical examples are presented for the analysis of a 3-DOF planar platform-type and of a 6-DOF spatial “Stewart Platform” manipulators to illustrate the analysis procedure.

scholarly journals Optical axes of catadioptric systems including visual, Purkinje and other nonvisual systems of a heterocentric astigmatic eye

2010 ◽  
Vol 69 (3) ◽  
Author(s):  
W. F. Harris
Keyword(s):  
Visual System ◽  
Optical Axis ◽  
The Other ◽  
Optical Systems ◽  
Numerical Examples ◽  
Straight Line ◽  
Optical Axes ◽  
Catadioptric Systems ◽  
Reflecting Surfaces ◽  
Special Case

For a dioptric system with elements which may be heterocentric and astigmatic an optical axis has been defined to be a straight line along which a ray both enters and emerges from the system.  Previous work shows that the dioptric system may or may not have an optical axis and that, if it does have one, then that optical axis may or may not be unique.  Formulae were derived for the locations of any optical axes.  The purpose of this paper is to extend those results to allow for reflecting surfaces in the system in addition to refracting elements.  Thus the paper locates any optical axes in catadioptric systems (including dioptric systems as a special case).  The reflecting surfaces may be astigmatic and decentred or tilted.  The theory is illustrated by means of numerical examples.  The locations of the optical axes are calculated for seven optical systems associated with a particular heterocentric astigmatic model eye.  The optical systems are the visual system, the four Purkinje systems and two other nonvisual systems of the eye.  The Purkinje systems each have an infinity of optical axes whereas the other nonvisual systems, and the visual system, each have a unique optical axis. (S Afr Optom 2010 69(3) 152-160)

scholarly journals MULTILEVEL NUMERICAL MODEL OF HIP JOINT ACCOUNTING FOR FRICTION IN THE HIP RESURFACING ENDOPROSTHESIS

2019 ◽  
Vol 17 (1) ◽  
pp. 29 ◽  
Author(s):  
Galina M. Eremina ◽  
Alexey Yu. Smolin
Keyword(s):  
Numerical Model ◽  
Multilevel Modeling ◽  
Operation Time ◽  
Scratch Test ◽  
Hip Resurfacing ◽  
Knee Joints ◽  
Macroscopic Model ◽  
Tribological Characteristics ◽  
Cellular Automaton Method ◽  
Moving Parts

Friction between the moving parts of the endoprosthesis has a significant impact on the endoprosthesis operation time. Primarily, it concerns the endoprosthesis of hip and knee joints. To improve the tribological characteristics of the metal endoprosthesis, hardening nanostructured coatings are used. Usually, titanium and titanium alloys are used as metal, and titanium nitride is used as a coating. Herein, we propose an approach to multilevel modeling of the system “bone-endoprosthesis” which is based on the movable cellular automaton method and accounts for friction between the moving parts of the hip resurfacing endoprosthesis. We validated the models of the friction system materials using the instrumented scratch test simulation. Then, we simulated friction at the mesolevel, explicitly considering roughness of the coating. The results obtained at the mesolevel were used as tribological characteristics of the coating in the macroscopic model of the hip resurfacing endoprosthesis.

Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks with Delays

2009 ◽  
Vol 21 (12) ◽  
pp. 3444-3459 ◽  
Author(s):  
Wei Lin
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Method ◽  
Autonomous Systems ◽  
Neural Systems ◽  
Stability Criteria ◽  
Volterra System ◽  
Numerical Examples ◽  
The Stability ◽  
Special Case

Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the [Formula: see text]-global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-Volterra system, an important prototype of competitive neural networks, as a special case. The stability criteria for autonomous systems then follow as a corollary. Two numerical examples are provided to show that the limiting equilibrium or periodic solution need not be positive.

Two-Dimensional Numerical Model for Studies of Collective Beam-Plasma Interaction

2010 ◽  
Vol 5 (2) ◽  
pp. 85-97
Author(s):  
Andrey V. Terekhov ◽  
Igor V. Timofeev ◽  
Konstantin V. Lotov
Keyword(s):  
Numerical Model ◽  
Electron Beams ◽  
Modulational Instability ◽  
Two Dimensional ◽  
Particle In Cell ◽  
Plasma Energy ◽  
Proposed Model ◽  
The Laplace Operator ◽  
Physical Phenomena ◽  
Powerful Electron

A two-dimensional particle-in-cell numerical model is developed to simulate collective relaxation of powerful electron beams in plasmas. To increase the efficiency of parallel particle-in-cell simulations on supercomputers, the Dichotomy Algorithm is used for inversion of the Laplace operator. The proposed model is tested with several well-known physical phenomena and is shown to adequately simulate basic effects of the beam driven turbulence. Also, the modulational instability is studied in the regime when the energy of pumping wave significantly exceeds the thermal plasma energy

Creep of the Plane Steel Frame at Elevated Temperature

2012 ◽  
Vol 446-449 ◽  
pp. 793-796
Author(s):  
Hui Zhu ◽  
Yu Ching Wu
Keyword(s):  
Numerical Model ◽  
Significant Contribution ◽  
Geometrical Nonlinearity ◽  
Steel Frames ◽  
Steel Structures ◽  
Element Formulation ◽  
Numerical Examples ◽  
Lagrangian Finite Element ◽  
In Fire ◽  
Plane Steel Frame

In this paper, co-rotational total Lagrangian finite element formulation is derived, and the corresponding numerical model is developed to study creeping behavior of plane steel frames in fire. Geometrical nonlinearity, material nonlinearity, high temperature creeping, and temperature rising rate are taken into account. To verify accuracy and efficiency of the numerical model, four prototypical numerical examples are analyzed using this model. Results are in a great agreement with solutions in literatures. Then the numerical model is used to analyze creeping behavior of the plane steel frames when temperature is lowering. The numerical results have significant contribution to resistance and protection for steel structures against disastrous fires.

Asymmetric two-dimensional jet efflux from a channel

1977 ◽  
Vol 80 (1) ◽  
pp. 1-15
Author(s):  
C. Samuel Martin
Keyword(s):  
Experimental Data ◽  
Analytical Approach ◽  
Two Dimensional ◽  
Asymmetric Case ◽  
Hodograph Plane ◽  
Single Jet ◽  
Von Mises ◽  
Two Jets ◽  
Direct Use ◽  
Special Case

Irrotational flow of two-dimensional jets from a channel is treated without direct use of a logarithmic hodograph plane. An analytical approach is introduced for solving the general problem of two jets issuing from a channel with three end plates. Numerical values of the contraction coefficient and the angle of jet deflexion are obtained for the special case where the two jets are located symmetrically and all the end plates are in line. Limiting cases of the resulting single-jet problem are the symmetric and asymmetric configurations solved by von Mises. Results for the asymmetric case improve upon the theoretical values reported by von Mises, and compare favourably with existing experimental data.

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