Stochastic stress-based topology optimization of structural frames based upon the second deviatoric stress invariant

2020 ◽  
Vol 224 ◽  
pp. 111186
Author(s):  
Navid Changizi ◽  
Gordon P. Warn
Keyword(s):  
Topology Optimization ◽  
Deviatoric Stress ◽  
Structural Frames ◽  
Stress Invariant

Thermoviscoplasticity Theory Incorporating the Third Deviatoric Stress Invariant

2015 ◽  
Vol 51 (1) ◽  
pp. 85-91 ◽  
Author(s):  
M. E. Babeshko ◽  
Yu. N. Shevchenko ◽  
N. N. Tormakhov
Keyword(s):  
Deviatoric Stress ◽  
The Third ◽  
Stress Invariant

scholarly journals A quadratic viscous fluid law for ice deduced from Steinemann's uni-axial compression and torsion experiments

2021 ◽  
pp. 1-11
Author(s):  
R. Staroszczyk ◽  
L. W. Morland
Keyword(s):  
Viscous Fluid ◽  
Strain Rate ◽  
Axial Stress ◽  
Deviatoric Stress ◽  
Quadratic Term ◽  
Quadratic Relation ◽  
Stress And Strain Rate ◽  
Stress Invariant ◽  
Rate Formulation ◽  
Rule Out

Abstract The response of ice to applied stress on ice-sheet flow timescales is commonly described by a non-linear incompressible viscous fluid, for which the deviatoric stress has a quadratic relation in the strain rate with two response coefficient functions depending on two principal strain-rate invariants I2 and I3. Commonly, a coaxial (linear) relation between the deviatoric stress and strain rate, with dependence on one strain-rate invariant I2 in a stress formulation, equivalently dependence on one deviatoric stress invariant in a strain-rate formulation, is adopted. Glen's uni-axial stress experiments determined such a coaxial law for a strain-rate formulation. The criterion for both uni-axial and shear data to determine the same relation is determined. Here, we apply Steinemann's uni-axial stress and torsion data to determine the two stress response coefficients in a quadratic relation with dependence on a single invariant I2. There is a non-negligible quadratic term for some ranges of I2; that is, a coaxial relation with dependence on one invariant is not valid. The data does not, however, rule out a coaxial relation with dependence on two invariants.

Allowing for the Third Deviatoric Stress Invariant in Analyzing the Deformation of Thin Shells

2018 ◽  
Vol 54 (2) ◽  
pp. 163-171 ◽  
Author(s):  
M. E. Babeshko ◽  
V. G. Savchenko
Keyword(s):  
Deviatoric Stress ◽  
Thin Shells ◽  
The Third ◽  
Stress Invariant

Residual Stress Analysis of the Autofrettaged Thick-Walled Tube Using Nonlinear Kinematic Hardening

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
G. H. Farrahi ◽  
George Z. Voyiadjis ◽  
S. H. Hoseini ◽  
E. Hosseinian
Keyword(s):  
Plastic Deformation ◽  
Residual Stresses ◽  
Stress Tensor ◽  
Kinematic Hardening ◽  
Deviatoric Stress ◽  
Material Behavior ◽  
Behavior Modeling ◽  
The Third ◽  
Deviatoric Stress Tensor ◽  
Stress Invariant

Recent research indicates that accurate material behavior modeling plays an important role in the estimation of residual stresses in the bore of autofrettaged tubes. In this paper, the material behavior under plastic deformation is considered to be a function of the first stress invariant in addition to the second and the third invariants of the deviatoric stress tensor. The yield surface is assumed to depend on the first stress invariant and the Lode angle parameter which is defined as a function of the second and the third invariants of the deviatoric stress tensor. Furthermore for estimating the unloading behavior, the Chaboche's hardening evolution equation is modified. These modifications are implemented by adding new terms that include the effect of the first stress invariant and pervious plastic deformation history. For evaluation of this unloading behavior model a series of loading-unloading tests are conducted on four types of test specimens which are made of the high-strength steel, DIN 1.6959. In addition finite element simulations are implemented and the residual stresses in the bore of a simulated thick-walled tube are estimated under the autofrettage process. In estimating the residual stresses the effect of the tube end condition is also considered.

A Plasticity Model for Metals With Dependency on All the Stress Invariants

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
George Z. Voyiadjis ◽  
S. H. Hoseini ◽  
G. H. Farrahi
Keyword(s):  
Yield Criterion ◽  
High Strength ◽  
Experimental Tests ◽  
Deviatoric Stress ◽  
Cyclic Behavior ◽  
Isotropic Hardening ◽  
Plasticity Model ◽  
Mapping Algorithm ◽  
The Third ◽  
Stress Invariant

Recent experiments on metals have shown that all of the stress invariants should be involved in the constitutive description of the material in plasticity. In this paper, a plasticity model for metals is defined for isotropic materials, which is a function of the first stress invariant in addition to the second and the third invariants of the deviatoric stress tensor. For this purpose, the Drucker–Prager yield criterion is extended by addition of a new term containing the second and the third deviatoric stress invariants. Furthermore for estimating the cyclic behavior, new terms are incorporated into the Chaboche's hardening evolution equation. These modifications are applied by adding new terms that include the effect of pervious plastic history of deformation on the current hardening evaluation equation. Also modified is the isotropic hardening rule with incorporating the effect of the first stress invariant. For calibration and evaluation of this plasticity model, a series of experimental tests are conducted on high strength steel, DIN 1.6959. In addition, finite element simulations are carried out including integration of the constitutive equations using the modified return mapping algorithm. The modeling results are in good agreement with experiments.

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