Rheological Equations for Synovial Fluids

1978 ◽  
Vol 100 (4) ◽  
pp. 169-186 ◽  
Author(s):  
W. M. Lai ◽  
S. C. Kuei ◽  
V. C. Mow
Keyword(s):  
Constitutive Equations ◽  
Synovial Joint ◽  
Integral Type ◽  
Material Parameters ◽  
Material Functions ◽  
Synovial Fluids ◽  
Joint Biomechanics ◽  
Differential Type ◽  
The Many ◽  
Rate Type

This review examines a number of theoretical constitutive equations which are applicable to the description of rheological behaviors of synovial fluids. These equations include the integral type, the rate type, the differential type and the generalized new-tonian fluid. Explicit values of the material parameters and/or material functions appearing in these equations are obtained from the many rheological measurements on synovial fluids of the literature. Many of the values of these parameters are taken from the literature, but some are newly computed values obtained by the present authors to make the list of available constitutive equations more extensive, using the existing experimental data. It is hoped that the diversity of the constitutive equations presented here and their appropriate material constants and/or functions will afford researchers in the field of synovial joint biomechanics the choice of a particular constitutive model for synovial fluid to meet their specific purpose.

An instability in some rate-type viscoelastic constitutive equations

1967 ◽  
Vol 22 (8) ◽  
pp. 1079-1082 ◽  
Author(s):  
R.I. Tanner ◽  
J.M. Simmons
Keyword(s):  
Constitutive Equations ◽  
Rate Type

Modelling of Cyclic Plasticity and Viscoplasticity of Directionally Solified DZ125 Superalloy: Part I: Estimating the Parameters of Chaboche Constitutive Equations

2011 ◽  
Vol 295-297 ◽  
pp. 854-858
Author(s):  
Jie Qiong Li ◽  
Li Jun Wang
Keyword(s):  
Constitutive Model ◽  
Test Data ◽  
Creep Test ◽  
Constitutive Equations ◽  
Least Square ◽  
Cyclic Plasticity ◽  
Initial Material ◽  
Material Parameters ◽  
Cyclic Relaxation ◽  
Least Square Procedure

Cyclic plasticity and viscoplasticity of directionally solified superalloy, DZ125, have been described using the Chaboche unified constitutive model. A set of initial material parameters has been determined utilizing the monotonic, cyclic, relaxation and creep test data of DZ125 at 980°C, while an optimum set of material parameters has been obtained by means of least-square procedure.

scholarly journals Logarithmic Spin, Logarithmic Rate and Material Frame-Indifferent Generalized Plasticity

2016 ◽  
Vol 08 (05) ◽  
pp. 1650060 ◽  
Author(s):  
D. Soldatos ◽  
S. P. Triantafyllou
Keyword(s):  
Constitutive Equations ◽  
Integration Scheme ◽  
Spatial Form ◽  
Numerical Examples ◽  
Material Frame Indifference ◽  
Generalized Plasticity ◽  
Analysis On Manifolds ◽  
Computational Implementation ◽  
Material Frame ◽  
Rate Type

In this work, we present a new rate type formulation of large deformation generalized plasticity which is based on the consistent use of the logarithmic rate concept. For this purpose, the basic constitutive equations are initially established in a local rotationally neutralized configuration which is defined by the logarithmic spin. These are then rephrased in their spatial form, by employing some standard concepts from the tensor analysis on manifolds. Such an approach, besides being compatible with the notion of (hyper)elasticity, offers three basic advantages, namely: (i) The principle of material frame-indifference is trivially satisfied. (ii) The structure of the infinitesimal theory remains essentially unaltered. (iii) The formulation does not preclude anisotropic response. A general integration scheme for the computational implementation of generalized plasticity models which are based on the logarithmic rate is also discussed. The performance of the scheme is tested by two representative numerical examples.

scholarly journals Inelastic Material Models of Type 316H for Elevated Temperature Design of Advanced High Temperature Reactors

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4548
Author(s):  
Gyeong-Hoi Koo ◽  
Ji-Hyun Yoon
Keyword(s):  
High Temperature ◽  
Elevated Temperature ◽  
Constitutive Equations ◽  
Isotropic Hardening ◽  
Material Models ◽  
Material Parameters ◽  
Hardening Behavior ◽  
Inelastic Material ◽  
High Temperature Reactors ◽  
Elevated Temperature Design

In this paper, the inelastic material models for Type 316H stainless steel, which is one of the principal candidate materials for elevated temperature design of the advanced high temperature reactors (HTRs) pressure retained components, are investigated and the required material parameters are identified to be used for both elasto-plastic models and unified viscoplastic models. In the constitutive equations of the inelastic material models, the kinematic hardening behavior is expressed with the Chaboche model with three backstresses, and the isotropic hardening behavior is expressed by the Voce model. The required number of material parameters is minimized to be ten in total. For the unified viscoplastic model, which can express both the time-independent plastic behavior and the time-dependent viscous behavior, the constitutive equations have the same kinematic and isotropic hardening parameters of the elasto-plastic material model with two additional viscous parameters. To identify the material parameters required for these constitutive equations, various uniaxial tests were carried out at isothermal conditions at room temperature and an elevated temperature range of 425–650 °C. The identified inelastic material parameters were validated through the comparison between tests and calculations.

Constitutive Equations for Mg Alloy Hot Work Modeling

2008 ◽  
Vol 604-605 ◽  
pp. 53-65 ◽  
Author(s):  
H.J. McQueen ◽  
Paola Leo ◽  
Emanuela Cerri
Keyword(s):  
Constitutive Equations ◽  
Flow Curve ◽  
Grain Morphology ◽  
Hot Working ◽  
Mg Alloys ◽  
Mg Alloy ◽  
Curve Shape ◽  
Material Parameters ◽  
Tension Tests ◽  
Constitutive Parameters

Constitutive equations for hot working are of great importance in optimizing forming processes to balance reductions in preheating and force, to avoid defects and to improve properties. Flow curve shapes and. constitutive parameters are affected by variations in composition, in homogenization, in grain morphology and significantly in texture. Confidence in published analyses is enhanced by existence of many data for the same or similar alloys. In this paper, constitutive equations have been collected for commercial Mg alloys from torsion, compression and tension tests in the range from 10-3 to 10 s-1 and 180 – 500°C. Some data were determined by the authors’ but more came from published reports; in some cases they have been re-calculated in a common manner. The deformation and restoration mechanisms that control the flow curve shape and the material parameters are summarized. Microstructure investigations of strained samples are illustrated. Applications to extrusion or rolling are discussed; comparisons to Al are made as appropriate.

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