Hypo-elasticity and plasticity

1956 ◽  
Vol 234 (1196) ◽  
pp. 46-59 ◽  
Keyword(s):  
General Theory ◽  
Constitutive Equations ◽  
Work Hardening ◽  
Strain Curve ◽  
Simple Extension ◽  
Logarithmic Strain ◽  
Elasticity Equations ◽  
Plastic Materials ◽  
Special Case

A general theory of work-hardening incompressible plastic materials is developed as a special case of Truesdell’s theory of hypo-elasticity. Equations are given in general coordinates for a single loading followed by one unloading, and attention is directed to materials for which the stress-logarithmic strain curve for unloading in simple extension is linear. Using a particular case of the corresponding constitutive equations for loading, which is a generalization of that suggested by Prager, applications are made to a number of specific problems.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Modeling the Stress-Strain Curve of Elastic-Plastic Materials

2021 ◽  
Vol 316 ◽  
pp. 936-941
Author(s):  
Natalya Ya. Golovina
Keyword(s):  
Mathematical Models ◽  
Strain Curve ◽  
Variational Model ◽  
Linear Deformation ◽  
Plastic Materials ◽  
Non Linear ◽  
Linear Sections ◽  
Elastic Plastic Materials ◽  
Deformation Section ◽  
St3sp Steel

The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.

The behaviour of supersonic flow past a body of revolution, far from the axis

1950 ◽  
Vol 201 (1064) ◽  
pp. 89-109 ◽  
Keyword(s):  
Supersonic Flow ◽  
General Theory ◽  
Body Of Revolution ◽  
Flow Past ◽  
Physical Importance ◽  
Special Case ◽  
Pointed Body ◽  
Asymptotic Forms

A theory is developed of the supersonic flow past a body of revolution at large distances from the axis, where a linearized approximation is valueless owing to the divergence of the characteristics at infinity. It is used to find the asymptotic forms of the equations of the shocks which are formed from the neighbourhoods of the nose and tail. In the special case of a slender pointed body, the general theory at large distances is used to modify the linearized approximation to give a theory which is uniformly valid at all distances from the axis. The results which are of physical importance are summarized in the conclusion (§ 9) and compared with the results of experimental observations.

scholarly journals Material Characteristics Evaluation for DC04-Welded Tube Hydroforming

2021 ◽  
Author(s):  
Liqun Niu ◽  
Qi Zhang ◽  
Bin Han
Keyword(s):  
Work Hardening ◽  
Tube Hydroforming ◽  
Strain Curve ◽  
Prediction Equation ◽  
Approximate Determination ◽  
Test Machine ◽  
Sheet Blank ◽  
Material Characteristics ◽  
Welded Tube ◽  
Strain Stress

Abstract Tube hydroforming (THF) technology is widely applied, especially in the automotive and aircraft industries. Material characteristics of tubular workpieces should be evaluated in terms of bending and THF processes. A mathematical model, which combines the assumption of elliptical contour of a bulged wall and the prediction equation of wall thickness, is provided to analyze the THF process and to obtain the strain-stress relationship of tubes. Material characteristics of a DC04-welded tube is obtained by using a self-designed THF test machine. Considering the effects of pre-work hardening, we discuss the material strain-stress relationships of the tube and original sheet blank. An approximate determination method is proposed to obtain the stress-strain curve of the tube by using the curve of the original sheet blank and the hardness of the tube and sheet blank. A suitable constitutive equation with pre-work hardening is applied to the DC04-welded tubes through simulation and experimental methods.

Some Properties of a Mechanical Model of Plasticity

1948 ◽  
Vol 15 (3) ◽  
pp. 222-225
Author(s):  
H. F. Bohnenblust ◽  
Pol Duwez
Keyword(s):  
Plastic Deformation ◽  
Potential Energy ◽  
Work Hardening ◽  
Mechanical Model ◽  
Strain Curve ◽  
Hysteresis Curve ◽  
Plastic Range ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Mechanical Models

Abstract Various mechanical models explaining the plastic deformation of metals have been proposed. One of the present authors has shown that in some cases an analytical expression for the stress-strain curve and the hysteresis curve of a metal in the plastic range can be deduced from such a model. The present investigation is a further analysis of the model leading to the computation of the change in potential energy of the metal due to work-hardening.

On Pólya's Theorem

1967 ◽  
Vol 19 ◽  
pp. 792-799 ◽  
Author(s):  
J. Sheehan
Keyword(s):  
Finite Groups ◽  
Scalar Product ◽  
Combinatorial Analysis ◽  
Simple Extension ◽  
Group Characters ◽  
Polya's Theorem ◽  
Representations Of Finite Groups ◽  
Pólya’S Theorem ◽  
Special Case ◽  
Superposition Theorem

In 1927 J. H. Redfield (9) stressed the intimate interrelationship between the theory of finite groups and combinatorial analysis. With this in mind we consider Pólya's theorem (7) and the Redfield-Read superposition theorem (8, 9) in the context of the theory of permutation representations of finite groups. We show in particular how the Redfield-Read superposition theorem can be deduced as a special case from a simple extension of Pólya's theorem. We give also a generalization of the superposition theorem expressed as the multiple scalar product of certain group characters. In a later paper we shall give some applications of this generalization.

scholarly journals Congruences induced by transitive representations of inverse semigroups

1987 ◽  
Vol 29 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Mario Petrich ◽  
Stuart Rankin
Keyword(s):  
General Theory ◽  
Inverse Semigroup ◽  
Symmetric Group ◽  
Transitive Group ◽  
Inverse Semigroups ◽  
Group Representations ◽  
Symmetric Inverse Semigroup ◽  
The Right ◽  
Special Case

Transitive group representations have their analogue for inverse semigroups as discovered by Schein [7]. The right cosets in the group case find their counterpart in the right ω-cosets and the symmetric inverse semigroup plays the role of the symmetric group. The general theory developed by Schein admits a special case discovered independently by Ponizovskiǐ [4] and Reilly [5]. For a discussion of this topic, see [1, §7.3] and [2, Chapter IV].

Modelling of Cyclic Plasticity With Unified Constitutive Equations: Improvements in Simulating Normal and Anomalous Bauschinger Effects

1980 ◽  
Vol 102 (2) ◽  
pp. 215-222 ◽  
Author(s):  
A. K. Miller
Keyword(s):  
Constitutive Equations ◽  
Work Hardening ◽  
Hysteresis Loops ◽  
Experimental Tests ◽  
Cyclic Hardening ◽  
Back Stress ◽  
Cyclic Softening ◽  
Cyclic Plasticity ◽  
Dislocation Loops ◽  
Work Hardening Coefficient

In simulating cyclic plasticity with several existing “unified” constitutive equations, the predicted hysteresis loops are “oversquare” with respect to experimentally-observed behavior. To eliminate this shortcoming in the constitutive equations developed by the present author, the work-hardening coefficient in the equation controlling the back stress (R) has been made a function of the back stress itself and the sign of the effective modulus-compensated stress σ/E – R. This improvement results in simulated hysteresis loops whose curvature closely resembles that in experimental tests. The improvement preserves all of the previously demonstrated capabilities such as cyclic hardening, cyclic hardening, cyclic softening, etc. The same equations can also simulate some unusual experimentally-observed Bauschinger effects involving local reversals in curvature. The curvature reversals in the simulations result from strain softening of the isotropic work-hardening variable in the equations. The physical significance of the behavior of the constitutive equations is discussed in terms of annihilation of previously-generated dislocation loops by reversing dislocations and experimentally-observed decreases in dislocation density and dissolution of cell walls upon stress reversal.

Sign in / Sign up

Export Citation Format

Share Document