Note on Maxwell's field equations and the constitutive equations

1966 ◽  
Vol 54 (9) ◽  
pp. 1210-1210
Author(s):  
R.C. Costen ◽  
L.D. Staton
Keyword(s):  
Constitutive Equations ◽  
Field Equations

Topics in Finite Elasticity: Hyperelasticity of Rubber, Elastomers, and Biological Tissues—With Examples

1987 ◽  
Vol 40 (12) ◽  
pp. 1699-1734 ◽  
Author(s):  
Millard F. Beatty
Keyword(s):  
Constitutive Equations ◽  
Mechanical Energy ◽  
Finite Elasticity ◽  
Physical Nature ◽  
Decomposition Theorem ◽  
Elastic Stability ◽  
Biological Tissues ◽  
Field Equations ◽  
Energy Principle ◽  
Hyperelastic Materials

This is an introductory survey of some selected topics in finite elasticity. Virtually no previous experience with the subject is assumed. The kinematics of finite deformation is characterized by the polar decomposition theorem. Euler’s laws of balance and the local field equations of continuum mechanics are described. The general constitutive equation of hyperelasticity theory is deduced from a mechanical energy principle; and the implications of frame invariance and of material symmetry are presented. This leads to constitutive equations for compressible and incompressible, isotropic hyperelastic materials. Constitutive equations studied in experiments by Rivlin and Saunders (1951) for incompressible rubber materials and by Blatz and Ko (1962) for certain compressible elastomers are derived; and an equation characteristic of a class of biological tissues studied in primary experiments by Fung (1967) is discussed. Sample applications are presented for these materials. A balloon inflation experiment is described, and the physical nature of the inflation phenomenon is examined analytically in detail. Results for the different materials are compared. Two major problems of finite elasticity theory are discussed. Some results concerning Ericksen’s problem on controllable deformations possible in every isotropic hyperelastic material are outlined; and examples are presented in illustration of Truesdell’s problem concerning analytical restrictions imposed on constitutive equations. Universal relations valid for all compressible and incompressible, isotropic materials are discussed. Some examples of non-uniqueness, including that of a neo-Hookean cube subject to uniform loads over its faces, are described. Elastic stability criteria and their connection with uniqueness in the theory of small deformations superimposed on large deformations are introduced, and a few applications are mentioned. Some previously unpublished results are presented throughout.

scholarly journals Principle of objectivity and classical physics

1979 ◽  
Vol 2 (1) ◽  
pp. 127-141
Author(s):  
M. Dutta ◽  
U. Basu
Keyword(s):  
Constitutive Equations ◽  
Field Equations ◽  
Classical Physics ◽  
General Field ◽  
Principle Of Objectivity

In literature, it is generally asserted that the “principle of objectivity” is valid for constitutive equations but not valid for general field equations. In this paper, the principle of objectivity is formulated clearly to emphasize the correct significance, and necessity of the principle and to discuss its validity in physical theories. A discussion is made to show how successfully the principle of objectivity is also applicable to non-relativistic classical physics.

Implementation of Viscoelastic Behavior in a Time Domain Boundary Element Formulation

1993 ◽  
Vol 46 (11S) ◽  
pp. S41-S46 ◽  
Author(s):  
M. Schanz ◽  
L. Gaul
Keyword(s):  
Boundary Element ◽  
Time Domain ◽  
Constitutive Equations ◽  
Domain Boundary ◽  
Equations Of Motion ◽  
Surrounding Medium ◽  
Viscoelastic Behavior ◽  
Element Formulation ◽  
Field Equations ◽  
Primary Interest

The boundary element method (BEM) provides a powerful tool for the calculation of elastodynamic response in frequency and time domain. Field equations of motion and boundary conditions are cast into integral equations, which are discretized only at the boundary. The boundary data often are of primary interest because they govern the transfer dynamics of members and the energy radiation into a surrounding medium. Formulations of BEM currently include conventional viscoelastic constitutive equations in the frequency domain. In the present paper viscoelastic behaviour is implemented in a time domain approach as well. The constitutive equations are generalized by taking fractional order time derivatives into account.

scholarly journals A mixture theory for geophysical fluids

2004 ◽  
Vol 11 (1) ◽  
pp. 75-82 ◽  
Author(s):  
A. C. Eringen
Keyword(s):  
Constitutive Equations ◽  
Degrees Of Freedom ◽  
Oil Spills ◽  
Initial Conditions ◽  
Mixture Theory ◽  
Continuum Theory ◽  
Second Law Of Thermodynamics ◽  
Heat Conducting ◽  
Field Equations ◽  
The Individual

Abstract. A continuum theory is developed for a geophysical fluid consisting of two species. Balance laws are given for the individual components of the mixture, modeled as micropolar viscous fluids. The continua allow independent rotational degrees of freedom, so that the fluids can exhibit couple stresses and a non-symmetric stress tensor. The second law of thermodynamics is used to develop constitutive equations. Linear constitutive equations are constituted for a heat conducting mixture, each species possessing separate viscosities. Field equations are obtained and boundary and initial conditions are stated. This theory is relevant to an atmospheric mixture consisting of any two species from rain, snow and/or sand. Also, this is a continuum theory for oceanic mixtures, such as water and silt, or water and oil spills, etc.

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