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.

A Review of Material Frame-Indifference in Mechanics

1998 ◽  
Vol 51 (8) ◽  
pp. 489-504 ◽  
Author(s):  
Charles G. Speziale
Keyword(s):  
Stress Tensor ◽  
Reynolds Stress ◽  
Continuum Mechanics ◽  
Constitutive Equations ◽  
Three Dimensional ◽  
Future Research ◽  
Invariance Group ◽  
Frame Indifference ◽  
Material Frame Indifference ◽  
Material Frame

The Principle of Material Frame-Indifference in various areas of mechanics is critically reviewed from a basic theoretical standpoint. Modern continuum mechanics is considered along with statistical mechanics and turbulence in an effort to better understand this commonly used axiom. It is argued that Material Frame-Indifference is a restricted invariance that can be highly useful in the formulation of constitutive equations but must be applied with caution. Material Frame-Indifference applies, in a strong approximate sense, to most areas of continuum mechanics where there is a clear cut separation of scales so that the ratio of fluctuating to mean time scales is extremely small. While it breaks down for the three-dimensional case, it rigorously applies to Reynolds stress models in the limit of two-dimensional turbulence where an analogy is made between the Reynolds stress tensor and the non-Newtonian part of the stress tensor in the laminar flow of a non-Newtonian fluid. On the other hand, the general invariance group of constitutive equations that is universally valid is the extended Galilean group of transformations which includes arbitrary time-dependent translations of the spatial frame of reference; rotational frame-dependence then enters exclusively through the intrinsic spin tensor. In order to definitively address this issue it is necessary to establish what the invariance group is of solutions to the fluctuation dynamics from which constitutive equations are formally constructed. The implications of these results for future research in a variety of different fields in mechanics are thoroughly discussed. This article includes 52 references.

scholarly journals Nonlinear viscoelasticity of strain rate type: an overview

2021 ◽  
Vol 477 (2245) ◽  
pp. 20200715
Author(s):  
Yasemin Şengül
Keyword(s):  
Strain Rate ◽  
Nonlinear Viscoelasticity ◽  
Rate Sensitivity ◽  
Point Of View ◽  
Daily Lives ◽  
Material Frame Indifference ◽  
Material Frame ◽  
Rate Type ◽  
Analysis Point

There are some materials in nature that experience deformations that are not elastic. Viscoelastic materials are some of them. We come across many such materials in our daily lives through a number of interesting applications in engineering, material science and medicine. This article concerns itself with modelling of the nonlinear response of a class of viscoelastic solids. In particular, nonlinear viscoelasticity of strain rate type, which can be described by a constitutive relation for the stress function depending not only on the strain but also on the strain rate, is considered. This particular case is not only favourable from a mathematical analysis point of view but also due to experimental observations, knowledge of the strain rate sensitivity of viscoelastic properties is crucial for accurate predictions of the mechanical behaviour of solids in different areas of applications. First, a brief introduction of some basic terminology and preliminaries, including kinematics, material frame-indifference and thermodynamics, is given. Then, considering the governing equations with constitutive relationships between the stress and the strain for the modelling of nonlinear viscoelasticity of strain rate type, the most general model of interest is obtained. Then, the long-term behaviour of solutions is discussed. Finally, some applications of the model are presented.

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

scholarly journals Implicit integration scheme for porous viscoplastic potential-based constitutive equations

2011 ◽  
Vol 10 ◽  
pp. 1544-1549 ◽  
Author(s):  
S. Msolli ◽  
O. Dalverny ◽  
J. Alexis ◽  
M. Karama
Keyword(s):  
Constitutive Equations ◽  
Integration Scheme ◽  
Implicit Integration

Constitutive relations for polar continua based on statistical mechanics and spatial averaging

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190407
Author(s):  
Bob Svendsen
Keyword(s):  
Angular Momentum ◽  
Constitutive Relations ◽  
Volume Averaging ◽  
Mass Point ◽  
Momentum Balance ◽  
Spatial Averaging ◽  
Material Frame Indifference ◽  
Phase Space Transport ◽  
Polar Continua ◽  
Material Frame

The purpose of the current work is the formulation of macroscopic constitutive relations, and in particular continuum flux densities, for polar continua from the underlying mass point dynamics. To this end, generic microscopic continuum field and balance relations are derived from phase space transport relations for expectation values of point fields related to additive mass point quantities. Given these, microscopic energy, linear momentum and angular momentum, balance relations are obtained in the context of the split of system forces into non-conservative and conservative parts. In addition, divergence–flux relations are formulated for the conservative part of microscopic supply-rate densities. For the case of angular momentum, two such relations are obtained. One of these is force-based, and the other is torque-based. With the help of physical and material theoretic restrictions (e.g. material frame-indifference), reduced forms of the conservative flux densities are obtained. In the last part of the work, formulation of macroscopic constitutive relations from their microscopic counterparts is investigated in the context of different spatial averaging approaches. In particular, these include (weighted) volume-averaging based on a localization function, surface averaging of normal flux densities based on Cauchy flux theory and volume averaging with respect to centre of mass.

Thermo-Elastoviscoplastic Buckling Behavior of Plates

1994 ◽  
Vol 61 (1) ◽  
pp. 169-175 ◽  
Author(s):  
G. J. Simitses ◽  
Y. Song
Keyword(s):  
Finite Element ◽  
Constitutive Equations ◽  
Material Models ◽  
Inelastic Buckling ◽  
Finite Element Approach ◽  
Numerical Examples ◽  
Initial Imperfections ◽  
Rate Dependent ◽  
Buckling Behavior ◽  
Element Approach

The thermo-elastoviscoplastic buckling behavior of plates is investigated. The analysis is based on nonlinear kinematic relations and nonlinear rate-dependent unified constitutive equations which include both Bodner-Partom’s and Walker’s material models. A finite element approach is employed to predict the inelastic buckling behavior. Numerical examples are given to demonstrate the effects of several parameters, which include temperature, small initial imperfections, and the thickness of the plate. Comparisons of buckling responses for the two models, Bodner-Partom’s and Walker’s, are also presented.

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