scholarly journals On the polar nature and invariance properties of a thermomechanical theory for continuum-on-continuum homogenization

2021 ◽  
pp. 108128652199432
Author(s):  
Kranthi K. Mandadapu ◽  
B. Emek Abali ◽  
Panayiotis Papadopoulos
Keyword(s):  
Heat Flux ◽  
Angular Momentum ◽  
Balance Laws ◽  
Polar Medium ◽  
Thermomechanical Theory ◽  
Form Invariance ◽  
Couple Stresses ◽  
Invariance Properties ◽  
Macroscopic Stress ◽  
The Continuum

This paper makes a rigorous case for considering the continuum derived by the homogenization of extensive quantities as a polar medium in which the balances of angular momentum and energy contain contributions due to body couples and couple stresses defined in terms of the underlying microscopic state. The paper also addresses the question of invariance of macroscopic stress and heat flux and form-invariance of the macroscopic balance laws.

scholarly journals A homogenization method for thermomechanical continua using extensive physical quantities

2012 ◽  
Vol 468 (2142) ◽  
pp. 1696-1715 ◽  
Author(s):  
Kranthi K. Mandadapu ◽  
Arkaprabha Sengupta ◽  
Panayiotis Papadopoulos
Keyword(s):  
Heat Flux ◽  
Continuum Mechanics ◽  
Equations Of Motion ◽  
Homogenization Method ◽  
Deformation Condition ◽  
Balance Laws ◽  
Macroscopic Stress ◽  
Stress Deformation ◽  
The One ◽  
Physical Quantities

This article proposes a continuum thermomechanical homogenization method inspired by the Irving–Kirkwood procedure relating the atomistic equations of motion to the balance laws of continuum mechanics. This method yields expressions for the macroscopic stress and heat flux in terms of microscopic kinematic and kinetic quantities. The resulting equation for macroscopic stress affords a rational comparison with the widely used Hill–Mandel stress-deformation condition, while the one for heat flux reduces, under certain assumptions, to a Hill–Mandel-like condition involving heat flux and the gradient of temperature.

A unified procedure for construction of theories of deformable media. III. Mixtures of interacting continua

1995 ◽  
Vol 448 (1934) ◽  
pp. 379-388 ◽  
Keyword(s):  
Single Phase ◽  
Balance Laws ◽  
First Law Of Thermodynamics ◽  
Thermomechanical Theory ◽  
Form Invariance ◽  
Deformable Media ◽  
Basic Equations

This paper is a continuation of parts I and II under the same title (Green & Naghdi 1995 a , b , Proc . R . Soc . Lond . A 448, 335, 357). In contrast to the earlier two papers which dealt with single phase continua, this paper is concerned with a new thermomechanical theory of multiphase interacting continua. We use the same unified procedure as in part I but now the various energies that enter the balance of energy must be modified to accommodate energetic contributions arising from N interacting finite constituents. Again, our derivation of the various basic balance laws is effected by an appeal to the form invariance of the balance of energy and leads to a system of basic equations of mixtures which are automatically consistent with the balance of energy or the first law of thermodynamics for mixtures of N constituents.

scholarly journals The Interaction of Rotation with Convection

1970 ◽  
Vol 4 ◽  
pp. 30-36
Author(s):  
Bernard R. Durney
Keyword(s):  
Heat Flux ◽  
Angular Momentum ◽  
Heat Transport ◽  
Differential Rotation ◽  
Initial Value Problem ◽  
List Type ◽  
Reynolds Stresses ◽  
Initial Value ◽  
Convective Cells ◽  
Flux Difference

AbstractThe equations for a rotating convective spherical shell are solved in the Herring approximation as an initial value problem. The main results are (1)The most unstable modes (those that maximize the heat flux) correspond to convective cells stretching from pole to pole.(2)The calculations of the Reynolds stresses show transport of angular momentum towards the equator. That is, differential rotation sets in with equatorial acceleration.(3)The convective heat transport is maximum at the equator. This would give rise to an equator-pole flux difference.(4)If convection is non-axisymmetric (as in the most unstable modes) there are no time independent solutions. The time dependence is oscillatory and of the form ωt + mφ.

AN ACTION PRINCIPLE FOR MAGNETOHYDRODYNAMICS

1963 ◽  
Vol 41 (12) ◽  
pp. 2241-2251 ◽  
Author(s):  
M. G. Calkin
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Magnetic Induction ◽  
Vector Potential ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Action Principle ◽  
Invariance Properties ◽  
Conservation Of Momentum

The equations of motion of an inviscid, infinitely conducting fluid in an electromagnetic field are transformed into a form suitable for an action principle. An action principle from which these equations may be derived is found. The conservation laws follow from invariance properties of the action. The space–time invariances lead to the conservation of momentum, energy, angular momentum, and center of mass, while the gauge invariances lead to conservation of mass, a generalization of the Helmholtz vortex theorem of hydrodyanmics, and the conservation of the volume integrals of A∙B and v∙B, where A is the vector potential, B is the magnetic induction, and v is the fluid velocity.

scholarly journals Configurational balance laws for dynamical fracture

2002 ◽  
pp. 205-220 ◽  
Author(s):  
V.K. Kalpakides ◽  
E.K. Agiasofitou
Keyword(s):  
Angular Momentum ◽  
Energy Release Rate ◽  
Continuum Mechanics ◽  
Release Rate ◽  
Propagation Velocity ◽  
Balance Laws ◽  
Balance Equations ◽  
Moving Crack ◽  
Material Force ◽  
Crack Propagation Velocity

In the spirit of modern continuum mechanics, global balance laws for momentum, angular momentum, energy and pseudomomentum are formulated for an elastic body in the presence of a moving crack. Upon localization, the corresponding balance equations in the bulk and at the crack tip are simultaneously obtained. The proposed framework is convenient for the derivation of the well-known formula, which relates the crack propagation velocity, the global material force and the energy release rate. .

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