The Yield Condition and Flow Rule for a Metal Subjected to Finite Elastic Volume Change

1971 ◽  
Vol 93 (4) ◽  
pp. 708-712 ◽  
Author(s):  
J. B. Haddow ◽  
T. M. Hrudey
Keyword(s):  
Plastic Deformation ◽  
Hydrostatic Pressure ◽  
Plastic Flow ◽  
Volume Change ◽  
High Hydrostatic Pressure ◽  
Elastic Strain ◽  
Yield Condition ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Plastic Flow Rule

A theory for elastic-plastic deformation with finite elastic strain is outlined. The results of this theory are specialized to consider a metal subjected to high hydrostatic pressure which produces finite elastic volume change. Drucker’s postulate is used to obtain the form of the yield condition and the associated plastic flow rule.

Finite Elastic-Plastic Expansion of a Cylindrical Tube

1973 ◽  
Vol 2 (4) ◽  
pp. 216-222
Author(s):  
B. Slevinsky ◽  
J. B. Haddow
Keyword(s):  
Plastic Deformation ◽  
Yield Condition ◽  
Cylindrical Tube ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
End Conditions ◽  
Cylindrical Tubes ◽  
Limiting Case ◽  
Plastic Flow Rule

A numerical method for the analysis of the isothermal elastic-plastic expansion, by internal pressure, of cylindrical tubes with various end conditions is presented. The Tresca yield condition and associated plastic flow rule are assumed and both non-hardening and work-hardening tubes are considered with account being taken of finite plastic deformation. Tubes which undergo further plastic deformation on unloading are also considered. Expansion of a cylindrical cavity from zero radius in an infinite medium is considered as a limiting case.

Bifurcation in Elastic-Plastic Plates

1978 ◽  
Vol 5 (2) ◽  
pp. 79-88
Author(s):  
R.N. Dubey
Keyword(s):  
Plastic Deformation ◽  
Uniaxial Compression ◽  
Plastic Flow ◽  
Isotropic Material ◽  
Flow Rule ◽  
Material Behaviour ◽  
Incremental Theory ◽  
Elastic Plastic ◽  
Conventional Analysis ◽  
Plastic Flow Rule

It is shown that the isotropic material behaviour assumed in the classical incremental theory has two distinct implications, one for elastic deformation and another one for plastic deformation. This inconsistency has been removed by modifying the plastic-flow rule. The modified constitutive relation is used to calculate bifurcation stress in elastic-plastic plates under uniaxial compression. The bifurcation model used in the analysis is a generalized version of Shanley’s model – here restriction is placed on the amplitude of perturbation as opposed to restriction on the increase or rate of traction imposed in conventional analysis. The bifurcation stress thus obtained is significantly lower than the corresponding stress obtained from the classical incremental theory.

A new elastoplastic constitutive model for coarse granular aggregates incorporating particle breakage

2004 ◽  
Vol 41 (4) ◽  
pp. 657-671 ◽  
Author(s):  
Wadud Salim ◽  
Buddhima Indraratna
Keyword(s):  
Constitutive Model ◽  
Plastic Flow ◽  
Current Model ◽  
Particle Breakage ◽  
Flow Rule ◽  
Peak Strain ◽  
Stress Strain ◽  
Coarse Aggregates ◽  
Stress Changes ◽  
Plastic Flow Rule

A new elastoplastic stress–strain constitutive model is developed for granular coarse aggregates incorporating the degradation of particles during triaxial shearing. Coarse granular aggregates are subjected to breakage during excessive stress changes. Most of the available constitutive models do not consider the degradation of particles during shearing. In the current model, a plastic flow rule has been developed incorporating the energy consumption due to particle breakage during shear deformation. A non-associated flow and a kinematic type yield locus have been adopted in the model. A general formulation for the rate of particle breakage during shearing has been developed and incorporated in the plastic flow rule. The effects of particle breakage on the plastic distortional and volumetric deformations are incorporated in the current model. The stress–strain formulations are developed within the general critical state framework. The model can accurately predict the stress–strain and volume change behaviour of coarse granular aggregates. The plastic dilation and contraction features of coarse aggregates at various confining pressures are well captured, and the strain-hardening and post-peak strain-softening behaviour of coarse granular media is adequately represented. A particular feature of the model is its capability to predict the degree of particle breakage at any stage of shear deformation.Key words: constitutive modelling, coarse granular aggregates, particle breakage, dilatancy, non-associated flow, plasticity.

scholarly journals PLASTIC DEFORMATION OF THICK-WALLED SNOW-ICE CYLINDERS UNDER HYDROSTATIC PRESSURE

1962 ◽  
Vol 40 (10) ◽  
pp. 1310-1318 ◽  
Author(s):  
H. H. G. Jellinek
Keyword(s):  
Activation Energy ◽  
Plastic Deformation ◽  
Hydrostatic Pressure ◽  
Strain Rate ◽  
Plastic Flow ◽  
Constant Pressure ◽  
Circumferential Stress ◽  
Sine Function ◽  
Kcal Mole ◽  
Flow Process

The results of experiments on the plastic deformation of hollow snow-ice cylinders, closed at one end, as a function of circumferential stress and temperature are discussed. Data are graphed on deformation as a function of time for a snow-ice cylinder under 7.03 and 14.06 kg/cm2 hydrostatic pressure at −4.5 °C, deformation as a function of hydrostatic pressure from 2.11 to 7.03 kg/cm2, and deformation as a function of temperature at a constant pressure of 10.55 kg/cm2. The natural strain rate of closure at constant circumferential stress and temperature was a constant, which varied with circumferential stress as a sine function and was "exponentially dependent on temperature, with an activation energy of 14.1 kcal/mole at an average circumferential stress of 3.1 kg/cm2. The experiments agree well with an earlier interpretation of the plastic flow process representing flow between grain boundaries.

Generalized plastic flow rule

2005 ◽  
Vol 21 (2) ◽  
pp. 321-351 ◽  
Author(s):  
K HASHIGUCHI
Keyword(s):  
Plastic Flow ◽  
Flow Rule ◽  
Plastic Flow Rule

scholarly journals Non-orthogonal elastoplastic constitutive model for sand with dilatancy

2021 ◽  
Author(s):  
Jingyu Liang ◽  
Dechun Lu ◽  
Xiuli Du ◽  
Wei Wu ◽  
Chao Ma
Keyword(s):  
Constitutive Model ◽  
Plastic Flow ◽  
Flow Direction ◽  
Model Performance ◽  
Yield Function ◽  
Flow Rule ◽  
Shear Process ◽  
Hardening Parameter ◽  
Elastoplastic Constitutive Model ◽  
Plastic Flow Rule

A non-orthogonal elastoplastic constitutive model for sand with dilatancy is presented in the characteristic stress space. Dilatancy of sand is represented by the direction of plastic flow, which can be directly determined by applying the non-orthogonal plastic flow rule to an improved elliptic yield function. A new hardening parameter is developed to describe the contractive and dilative volume change during the shear process, which is co-ordinated with the non-orthogonal plastic flow direction. The combination of the non-orthogonal plastic flow rule and the proposed hardening parameter renders the proposed model with the ability to reasonably describe the stress-strain relationship of sand with dilatancy. The model performance is evaluated by comparing with the experimental data of sand under triaxial stress conditions.

scholarly journals Non-orthogonal elastoplastic constitutive model with the critical state for clay

2021 ◽  
Author(s):  
Jingyu Liang ◽  
Dechun Lu ◽  
Xin Zhou ◽  
Xiuli Du ◽  
Wei Wu
Keyword(s):  
Plastic Flow ◽  
Critical State ◽  
Flow Direction ◽  
Volumetric Strain ◽  
Yield Function ◽  
Triaxial Tests ◽  
Flow Rule ◽  
Model Framework ◽  
Plastic Strain Increment ◽  
Plastic Flow Rule

A non-orthogonal elastoplastic model for clay is proposed by combining the non-orthogonal plastic flow rule with the critical state concept, and the model framework is presented from the perspective of the magnitude and direction of the plastic strain increment. The magnitude is obtained based on the improved elliptical yield function and the plastic volumetric strain dependent hardening parameter. The direction is determined by ap-plying the non-orthogonal plastic flow rule with the Riemann-Liouville fractional derivative to the yield function without the necessity of additional plastic potential function. The presented approach gives rise to a simple model for soil with five parameters. All parameters have clear physical meaning and can be easily identified by triaxial tests. The model performance is shown by analyzing the evolution process of the yield surface, the hardening rule and the plastic flow direction. The capability of the proposed model to capture the mechanical behaviours of clay with different stiffness is also confirmed by predicting test results from the literature.

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