Application of Objective Rates in Mechanical Modeling of Solids

1996 ◽  
Vol 63 (3) ◽  
pp. 692-698 ◽  
Author(s):  
W. D. Reinhardt ◽  
R. N. Dubey
Keyword(s):  
Simple Shear ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Logarithmic Strain ◽  
Mechanical Modeling ◽  
Rigid Plastic ◽  
Eulerian Strain ◽  
Objective Rate ◽  
Simple Shear Deformation ◽  
Objective Rates

A unified formulation is developed for deformation-related spins, and for objective rates based on them. The approach generalizes the underlying concepts, and allows new rates to be constructed. Mathematical and thermodynamical restrictions on these are shown. As a result, it can be demonstrated that the Eulerian strain rate is an objective rate of logarithmic strain, based on a spin easily derivable from the general form. Interrelations between other known spins and objective rates emerge very clearly. Consequences of the proposed formalism are explored in hypoelastic and in rigid-plastic constitutive relations, the latter involving purely isotropic and purely kinematic hardening. The application of the resulting models to the simple shear deformation is shown.

Stress Responses to Large Simple Shear Deformation in Elasticity Based on the Logarithmic Strain

2011 ◽  
Vol 488-489 ◽  
pp. 424-427
Author(s):  
Li Hong Yang ◽  
Jia Qu ◽  
Yun Zeng He
Keyword(s):  
Shear Stress ◽  
Constitutive Model ◽  
Shear Deformation ◽  
Simple Shear ◽  
Stress Responses ◽  
Large Strain ◽  
Small Deformation ◽  
Logarithmic Strain ◽  
Simple Shear Deformation ◽  
Objective Rates

The logarithmic strain is more suitable for analyzing large strain problems because the volume invariability condition in small deformation is equivalent to volume invariability condition in large deformation when using the logarithmic strain. Large simple shear deformation has always been used in the analysis of large strain problems. In this paper, elastic large strain constitutive model was introduced based on the logarithmic strain and large simple shear deformation was analyzed by using the constitutive model given in the paper. The stress responses to large simple shear deformation were derived corresponding to four objective rates of tensors. The results show that normal stresses may maintain good monotonicity, but there exists different levels of oscillation of shear stress corresponding to various objective rates, and there was the most severe oscillation of stress when adopting Jaumann rate. The objective rate should not be the only factor bringing about oscillation of shear stress.

Corotational Rates for Kinematic Hardening at Large Plastic Deformations

1983 ◽  
Vol 50 (3) ◽  
pp. 561-565 ◽  
Author(s):  
Y. F. Dafalias
Keyword(s):  
Simple Shear ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Back Stress ◽  
Analytical Form ◽  
Rigid Plastic ◽  
Plastic Deformations ◽  
Novel Approach ◽  
Rigid Plastic Material ◽  
Large Plastic Deformations

To illustate the effect of the choice of corotational rates at large plastic deformations, expressions for the stresses developing in large simple shear are obtained in closed analytical form under the assumptions of a rigid-plastic material response and a Mises type isotropically and kinematically hardening constitutive model for two different corotational rates applied to the stress and the back-stress tensors. The observed difference in the simple shear response and the relative merits of the foregoing and other corotational rates are discussed, and a novel approach is proposed based on Mandel’ work and the representation theorem for isotropic second-order antisymmetric tensor valued functions.

scholarly journals An alternative approach to finite deformation

2018 ◽  
Vol 16 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Marina Trajkovic-Milenkovic ◽  
Otto Bruhns
Keyword(s):  
Constitutive Relations ◽  
Time Derivative ◽  
Distinctive Features ◽  
Eulerian Description ◽  
Objective Time ◽  
Alternative Approach ◽  
Rate Form ◽  
Objective Rate ◽  
Finite Elastoplasticity ◽  
Objective Rates

In elastoplasticity formulation constitutive relations are usually given in rate form, i.e. they represent relations between stress rate and strain rate. The adopted constitutive laws have to stay independent in relation to the change of frame of reference, i.e. to stay objective. While the objectivity requirement in a material description is automatically satisfied, in an Eulerian description, especially in the case of large deformations, the objectivity requirement can be violated even for objective quantities. Thus, instead of a material time derivative in the Eulerian description objective time derivatives have to be implemented. In this work the importance of the objective rate implementation in the constitutive relations of finite elastoplasticity is clarified. Likewise, it shows the overview of the most frequently used objective rates nowadays, their advantages and shortcomings, as well as the distinctive features of the recently introduced logarithmic rate.

The Plastic Spin

1985 ◽  
Vol 52 (4) ◽  
pp. 865-871 ◽  
Author(s):  
Y. F. Dafalias
Keyword(s):  
Simple Shear ◽  
Large Deformations ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Stability Conditions ◽  
The Novel ◽  
Representation Theorems ◽  
Plastic Spin ◽  
Liapunov Method ◽  
Memory Type

A macroscopic formulation of large deformations elastoplasticity with tensorial structure variables is presented. The novel features are the effect of constitutive relations for the plastic spin and, to a lesser degree of importance, of elastically embedding the structure variables. The plastic spin constitutive relations are obtained for different kinds of initial and induced anisotropies on the basis of the representation theorems for isotropic second-order antisymmetric tensor-valued functions, and their role is illustrated by the analysis of several examples at large homogeneous deformations. In particular the analysis of simple shear with nonlinear kinematic hardening of the evanescent memory type provides, on the basis of the second Liapunov method for stability, conditions on the material constants for the occurrence or not of stress oscillations with monotonically increasing shear strain.

Some comments on objective rates of symmetric Eulerian tensors with application to Eulerian strain rates

2000 ◽  
Vol 139 (1-4) ◽  
pp. 91-103 ◽  
Author(s):  
A. Meyers ◽  
P. Schie�e ◽  
O. T. Bruhns
Keyword(s):  
Strain Rates ◽  
Eulerian Strain ◽  
Objective Rates

Shear properties of passive ventricular myocardium

2002 ◽  
Vol 283 (6) ◽  
pp. H2650-H2659 ◽  
Author(s):  
Socrates Dokos ◽  
Bruce H. Smaill ◽  
Alistair A. Young ◽  
Ian J. LeGrice
Keyword(s):  
Shear Deformation ◽  
Simple Shear ◽  
Ventricular Myocardium ◽  
Left Ventricular ◽  
Shear Deformations ◽  
Shear Properties ◽  
Nonlinear Viscoelastic ◽  
Myocardial Layers ◽  
Shear Modes ◽  
Simple Shear Deformation

We examined the shear properties of passive ventricular myocardium in six pig hearts. Samples (3 × 3 × 3 mm) were cut from adjacent regions of the lateral left ventricular midwall, with sides aligned with the principal material axes. Four cycles of sinusoidal simple shear (maximum shear displacements of 0.1–0.5) were applied separately to each specimen in two orthogonal directions. Resulting forces along the three axes were measured. Three specimens from each heart were tested in different orientations to cover all six modes of simple shear deformation. Passive myocardium has nonlinear viscoelastic shear properties with reproducible, directionally dependent softening as strain is increased. Shear properties were clearly anisotropic with respect to the three principal material directions: passive ventricular myocardium is least resistant to simple shear displacements imposed in the plane of the myocardial layers and most resistant to shear deformations that produce extension of the myocyte axis. Comparison of results for the six different shear modes suggests that simple shear deformation is resisted by elastic elements aligned with the microstructural axes of the tissue.

Twinning in pure Ti subjected to monotonic simple shear deformation

2012 ◽  
Vol 72 ◽  
pp. 24-36 ◽  
Author(s):  
W. Tirry ◽  
S. Bouvier ◽  
N. Benmhenni ◽  
W. Hammami ◽  
A.M. Habraken ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Simple Shear ◽  
Simple Shear Deformation

Technical development of simple shear deformation experiments using a deformation-DIA apparatus

2010 ◽  
Vol 21 (5) ◽  
pp. 523-531 ◽  
Author(s):  
Tomohiro Ohuchi ◽  
Takaaki Kawazoe ◽  
Norimasa Nishiyama ◽  
Nishihara Yu ◽  
Tetsuo Irifune
Keyword(s):  
Shear Deformation ◽  
Simple Shear ◽  
Technical Development ◽  
Simple Shear Deformation
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