An instability in some rate-type viscoelastic constitutive equations

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.

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Lubrication approximation of flows of a special class of non-Newtonian fluids defined by rate type constitutive equations

Applied Mathematical Modelling ◽

10.1016/j.apm.2018.03.038 ◽

2018 ◽

Vol 60 ◽

pp. 508-525 ◽

Cited By ~ 1

Author(s):

L. Fusi ◽

A. Farina ◽

G. Saccomandi ◽

K.R. Rajagopal

Keyword(s):

Constitutive Equations ◽

Special Class ◽

Newtonian Fluids ◽

Lubrication Approximation ◽

Rate Type

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

International Journal of Applied Mechanics ◽

10.1142/s1758825116500605 ◽

2016 ◽

Vol 08 (05) ◽

pp. 1650060 ◽

Cited By ~ 1

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.

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