Quantification of Numerical Stiffness for a Unified Viscoplastic Constitutive Model

1990 ◽  
Vol 112 (3) ◽  
pp. 271-276 ◽  
Author(s):  
S. M. Arnold
Keyword(s):  
Constitutive Model ◽  
State Space ◽  
Copper Alloy ◽  
Jacobian Matrix ◽  
The State ◽  
Maximum Difference ◽  
Material Parameters ◽  
State Variable ◽  
Variable Approach ◽  
State Point

Here the question of numerical stiffness pertaining to a unified viscoplastic constitutive model is examined. The viewpoint maintained throughout this study is the state variable approach. Stiffness is quantified by examining, analytically, the eigenvalues of the associated Jacobian matrix. Specific results, in the form of stiffness contours, for the material parameters characterizing the copper alloy NARloy-Z are presented in the associated uniaxial state space. The results indicate that the potential for numerical stiffness does exist, however the severity is highly dependent upon the location of the state point within the state space. Finally a qualitative analogy between the maximum difference in stiffness indicating eigenvalues and the G vectors of the corresponding state space is suggested.

scholarly journals Characteristic phenomena in combustion

1997 ◽  
Vol 1 (2) ◽  
pp. 147-159
Author(s):  
Dirk Meinköhn
Keyword(s):  
State Space ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
The State ◽  
State Variable ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Singularity Order ◽  
The Relationship ◽  
Stable Stationary Solutions

For the case of a reaction–diffusion system, the stationary states may be represented by means of a state surface in a finite-dimensional state space. In the simplest example of a single semi-linear model equation given. in terms of a Fredholm operator, and under the assumption of a centre of symmetry, the state space is spanned by a single state variable and a number of independent control parameters, whereby the singularities in the set of stationary solutions are necessarily of the cuspoid type. Certain singularities among them represent critical states in that they form the boundaries of sheets of regular stable stationary solutions. Critical solutions provide ignition and extinction criteria, and thus are of particular physical interest. It is shown how a surface may be derived which is below the state surface at any location in state space. Its contours comprise singularities which correspond to similar singularities in the contours of the state surface, i.e., which are of the same singularity order. The relationship between corresponding singularities is in terms of lower bounds with respect to a certain distinguished control parameter associated with the name of Frank-Kamenetzkii.

Sensitivities by the state variable approach

SIMULATION ◽  
1967 ◽  
Vol 8 (6) ◽  
pp. 337-343 ◽  
Author(s):  
Thomas W. Kerlin
Keyword(s):  
Frequency Response ◽  
The State ◽  
Efficient Procedure ◽  
State Variable ◽  
Sensitivity Equations ◽  
Variable Approach ◽  
Computer Calculations ◽  
Simple Matrix ◽  
Large Systems ◽  
Digital Computers

The well-known procedures for calculating transient-re sponse sensitivities, frequency-response sensitivities, and pole sensitivities have been successfully and profitably applied for several years. However, the usual formulations are not well suited for analysis of large systems on modern analog or digital computers. Expressions for these sensitivi ties are developed in this paper using simple matrix ma nipulations (usually referred to as the state variable ap proach). The state variable formulation illustrates clearly the structure of the sensitivity equations and provides an efficient procedure for computer calculations.

scholarly journals Textile Cover Effect on Aerodynamic Characteristics of a Paraglider Wing

2019 ◽  
Vol 27 (1(133)) ◽  
pp. 78-84
Author(s):  
Paulina Maślanka ◽  
Ryszard Korycki
Keyword(s):  
Numerical Simulations ◽  
Cross Section ◽  
Symmetry Plane ◽  
Aerodynamic Characteristics ◽  
The State ◽  
Plane Model ◽  
Material Parameters ◽  
Space Model ◽  
State Variable ◽  
Spline Curves

Defined herein are the two PA-fabrics covering a paraglider wing, with the comparative object being permeable clothing material. The material parameters of textiles are applied in numerical simulations of aerodynamic characteristics using the program ANSYS. The state variable is the pressure within the airfoil profile. The space model of a paraglider wing and plane model of its cross-section in the symmetry plane are analysed. The model was approximated by the coordinates of crucial points and smoothed by the spline-curves. The visualisation of stream filaments shows that it is advisable to cover the wing with the impermeable fabric.

A Constitutive Model for the Inelastic Multiaxial Response of Rene’ 80 at 871C and 982C

1990 ◽  
Vol 112 (2) ◽  
pp. 241-246 ◽  
Author(s):  
D. C. Stouffer ◽  
V. G. Ramaswamy ◽  
J. H. Laflen ◽  
R. H. Van Stone ◽  
R. Williams
Keyword(s):  
Constitutive Model ◽  
Experimental Results ◽  
Uniaxial Loading ◽  
Experimental Program ◽  
Multiaxial Loading ◽  
Loading Conditions ◽  
Nonproportional Loading ◽  
Material Parameters ◽  
State Variable

This paper contains an extension of the uniaxial state variable constitutive model of Ramaswamy et al. (1988) to the case of multiaxial loading. The correlation between uniaxial and multiaxial loading conditions is achieved through the assumptions of material isotropy and conservation of inelastic volume. The multiaxial extension is based only on the material parameters evaluated from uniaxial loading. The research is accompanied by a multiaxial experimental program to evaluate the response of Rene’ 80 at 871°C and 982° C. Experiments in the program include torsion, proportional axial and torsion, and nonproportional loading. It was shown experimentally that there is no extra hardening from the multiaxial loading than results from uniaxial loading. Further, it is shown that the multiaxial model is successful in predicting the experimental results using only the parameters determined from the uniaxial experiments.

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