Plane-Stress Analysis of the New Stress Tensor Decomposition

The accuracy and reliability of the new stress tensor decomposition to capture the plasticity behaviour of orthotropic materials under plane-stress conditions was examined in this paper. No experiment was required to perform this work. Therefore, the suitable, published paper which provides a relevant test result and sufficient material properties to characterise the new stress tensor decomposition, was used. This new stress tensor decomposition was used to presents a new yield criterion for orthotropic sheet metals under plane-stress conditions in this work. This was done by assuming the yield surface to be circular in the new deviatoric plane. The predictions of the new effectice stress expression were then compared with the experimental data of 6000 series aluminium alloy sheet (A6XXX-T4) and Al-killed cold-rolled steel sheet SPCE. The predicted new yield surfaces are in good agreement with respect to the experimental data for two materials (A6XXX-T4 and SPCE).

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Modelling of Shockwave Propagation in Orthotropic Materials

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.315.557 ◽

2013 ◽

Vol 315 ◽

pp. 557-561 ◽

Cited By ~ 9

Author(s):

Mohd Khir Mohd Nor ◽

Rade Vignjevic ◽

James Campbell

Keyword(s):

Stress Tensor ◽

Elastic Anisotropy ◽

Yield Criterion ◽

Plastic Anisotropy ◽

Deformation Gradient ◽

Tensor Decomposition ◽

Material Model ◽

Yield Function ◽

Orthotropic Materials ◽

Free Energy Function

Modelling of shockwave propagation in orthotropic materials requires an appropriate description of material behaviour within elastic and plastic regimes. To deal with this issues, a finite strain constitutive model for orthotropic materials was developed within a consistent thermodynamic framework of irreversible process in this paper. The important features of this material model are the multiplicative decomposition of the deformation gradient and a Mandel stress tensor combined with the new stress tensor decomposition generalised for orthotropic materials. The elastic free energy function and the yield function are defined within an invariant theory by means of the introduction of the structural tensors. The plastic behaviour is characterised within the associative plasticity framework using the Hills yield criterion. The complexity was further extended by coupling the formulation with the equation of state (EOS) to control the response of the material to shock loading. This material model which was developed and integrated in the isoclinic configuration provides a unique treatment for elastic and plastic anisotropy. The effects of elastic anisotropy are taken into account through the stress tensor decomposition and plastic anisotropy through yield surface defined in the generalized deviatoric plane perpendicular to the generalised pressure. To test its ability to describe shockwave propagation, the new material model was implemented into the LLNL-DYNA3D code. The results generated by the proposed material model were compared against the experimental Plate Impact test data of Aluminium Alloy 7010. A good agreement between experimental and simulation was obtained for two principal directions of material orthotropy.

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A Study of Yielding and Plasticity of Rapid Prototyped ABS

Mathematics ◽

10.3390/math9131495 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1495

Author(s):

Dan-Andrei Șerban ◽

Cosmin Marșavina ◽

Alexandru Viorel Coșa ◽

George Belgiu ◽

Radu Negru

Keyword(s):

Experimental Data ◽

Stress State ◽

Plastic Flow ◽

Plane Stress ◽

Yield Criterion ◽

Numerical Analyses ◽

Flow Potential ◽

Stress States ◽

State Configuration

In this article, the yielding and plastic flow of a rapid-prototyped ABS compound was investigated for various plane stress states. The experimental procedures consisted of multiaxial tests performed on an Arcan device on specimens manufactured through photopolymerization. Numerical analyses were employed in order to determine the yield points for each stress state configuration. The results were used for the calibration of the Hosford yield criterion and flow potential. Numerical analyses performed on identical specimen models and test configurations yielded results that are in accordance with the experimental data.

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Relations between cubic equation, stress tensor decomposition, and von Mises yield criterion

Applied Mathematics and Mechanics ◽

10.1007/s10483-015-1988-9 ◽

2015 ◽

Vol 36 (10) ◽

pp. 1359-1370

Author(s):

Haoyuan Guo ◽

Liyuan Zhang ◽

Yajun Yin ◽

Yongxin Gao

Keyword(s):

Stress Tensor ◽

Yield Criterion ◽

Tensor Decomposition ◽

Cubic Equation ◽

Von Mises Yield Criterion ◽

Von Mises

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A theory of the yield locus and flow rule of anisotropic materials

Journal of Strain Analysis ◽

10.1243/03093247v013204 ◽

1966 ◽

Vol 1 (3) ◽

pp. 204-215 ◽

Cited By ~ 5

Author(s):

T. C. Hsu

Keyword(s):

Experimental Data ◽

Linear Relationship ◽

Yield Stress ◽

Plane Stress ◽

Stress Ratio ◽

Yield Criterion ◽

Anisotropic Materials ◽

Yield Locus ◽

Flow Rule ◽

Stress Components

A general yield criterion for anisotropic materials is derived from the linear relationship between strain and stress components. The particular forms of the yield criterion for plane stress and for certain types of symmetry are discussed and are compared with available experimental data. The separate effects of the stress ratio and the direction of the stress axes on the yield stress are also determined.

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