A Finite Deformation Theory of Viscoplasticity Based on Overstress: Part I—Constitutive Equations

The viscoplasticity theory based on overstress (VBO) is extended to finite deformation (FVBO). Yield surfaces and loading/unloading conditions are not part of this theory which represents creep, relaxation, and rate sensitivity in a “unified” way. Additive decomposition of the rate of deformation into the elastic and the inelastic parts is assumed. For the elastic part, the hypoelastic relation is used. For the inelastic part, the flow law of VBO is augmented by a term quadratic in the overstress together with a modified Jaumann stress rate which jointly or separately allow the modeling of second-order effects.

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A Finite Deformation Theory of Viscoplasticity Based on Overstress: Part II—Finite Element Implementation and Numerical Experiments

Journal of Applied Mechanics ◽

10.1115/1.2897058 ◽

1990 ◽

Vol 57 (3) ◽

pp. 553-561 ◽

Cited By ~ 19

Author(s):

I. Nishiguchi ◽

T.-L. Sham ◽

E. Krempl

Keyword(s):

Finite Element ◽

Finite Deformation ◽

Numerical Experiments ◽

Deformation Theory ◽

Integration Method ◽

Time Integration ◽

Second Order ◽

Time Integration Method ◽

Finite Element Implementation ◽

Finite Deformation Theory

A one-step time integration method is developed for the finite deformation theory of viscoplasticity based on overstress (FVBO) described in Part I. This time integration method is based on a forward gradient approximation and it leads to explicit expressions of the tangent operators suitable for finite element implementation. Numerical experiments and closed-form solutions for a hypoelastic material in homogeneous deformation states are presented. The FVBO is applied to the modeling of second-order effects in torsion. The numerical results show that a modification of the Jaumann rate and second-order terms of the inelastic rate of deformation are necessary to model the observed effects.

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Comparison of Various Object Stress Rates under Simple Shear

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.650.407 ◽

2013 ◽

Vol 650 ◽

pp. 407-413 ◽

Cited By ~ 2

Author(s):

Dong Keon Kim ◽

Jong Wan Hu

Keyword(s):

Continuum Mechanics ◽

Simple Shear ◽

Finite Deformation ◽

Deformation Theory ◽

Numerical Results ◽

The Other ◽

Stress Rate ◽

Shear Problem ◽

Finite Deformation Theory ◽

Objective Stress

Object Stress rates to predict the behavior of material have been researched based on numerically and theoretically for researchers who study continuum mechanics due to its complexity. This study focused on the various objective stress rates which assumed the finite deformation theory. Eight object stress rates (Oldroyd, Truesdell, Cotter–Rivlin, Jaumann, Green–Naghdi, Eulerian, grangian, and logarithmic object stress rates) were introduced using continuum mechanics and analyzed to derive the numerical solution to the simple shear problem. Numerical results from each object stress rate were analyzed and compared with the results of the other stress rates. Finally, the appropriate object stress rate for the simple shear problem was determined based on the numerical results from eight objects stress rates.

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