Hi folks,
today I have been informed by the chief editor of the 'International
Journal of Modern Physics B' that three papers have been accepted for
publication at once:
ON THE SYSTEMATICS OF ENERGETIC TERMS IN CONTINUUM MECHANICS, AND A
NOTE ON GIBBS (1877) (date of acceptance May 24)
POTENTIAL THEORY AND ELASTICITY: A COMMENT ON GURTIN (1972) (May 24)
AN APPROACH TO DEFORMATION THEORY BASED ON THERMODYNAMIC PRINCIPLES
(May 6)
Abstract of 'Systematics & Gibbs':
The systematics of energetic terms as they are taught in continuum
mechanics deviate seriously from standard views in physics, resulting
in a profound misconception. It is demonstrated that the First Law of
Thermodynamics has been routinely re-interpreted in a sense that would
make it subordinate to Bernoulli's energy conservation law.
Furthermore, it is shown that the attempt by Gibbs to find a
thermodynamic understanding for elastic deformation does not
sufficiently account for all the energetic properties of such a
process.
Abstract of 'Gurtin':
In an exhaustive presentation of the linear theory of elasticity by
Gurtin (1972) the author included a chapter on the relation of the
theory of elasticity to the theory of potentials. Potential theory
distinguishes two fundamental physical categories: divergence-free and
divergence-involving problems. From the criteria given in the source
quoted by the author it is evident that elastic deformation of solids
falls into the latter category. It is documented in this short note
that the author presented volume-constant elastic deformation as a
divergence-free physical process, systematically ignoring all the
information that was available to him that this is not so.
In plain English: the guy cheated. He misled an entire generation of
scientists.
Abstract of 'Approach':
The Cauchy stress theory has been shown to be profoundly at variance
with the principles of the theory of potentials. Thus, a new physical
approach to deformation theory is presented which is based on the
balance of externally applied forces and material forces. The equation
of state is generalized to apply to solids, and transformed into
vector form. By taking the derivatives of an external potential and
the material internal energy with respect to the coordinates, two
vector fields are defined for the forces exerted by surrounding at the
system, subject to the boundary conditions, and vice versa, subject to
the material properties. These vector fields are then merged into a
third one that represents the properties of the loaded state. Through
the work function the force field is then directly transformed into
the displacement field. The approach permits fully satisfactory
prediction of all geometric and energetic properties of elastic and
plastic simple shear. It predicts the existence of a bifurcation at
the transition from reversible to irreversible behavior whose
properties permit correct prediction of cracks in solids. It also
offers a mechanism for the generation of sheath folds in plastic shear
zones and for turbulence in viscous flow. Finally, an example is given
how to apply the new approach to deformation of a discrete sample as a
function of loading configuration and sample shape.
Phenomena for which my approach delivers fully satisfactory
predictions are:
- S-C fabrics in mylonites,
- elastic-reversible dilatancy,
- orientation of joints in rocks,
- properties of microfabric diagrams for minerals with
simple geometric properties,
- the energetics of elastic and plastic pure shear and
simple shear
deformation, as they are known from experiments,
- the observed orientation of the regional stress field
in California around the San Andreas Fault,
- turbulence in viscous flow,
- generation of sheath folds in plastic shear zones,
- generation of cracks in brittle deformation.
Delivery of the three papers in paper print is scheduled for July. The
PDF files can be downloaded from my website,
www.elastic-plastic.de
Concerning the work done so far, based on Hooke, Euler, Cauchy,
Navier-Stokes, Prandtl-Reuss, Taylor-Bishop-Hill - It is going to be a
spectacle like the Hindenburg at Lakehurst. No regrets.
Falk Koenemann
Aachen, Germany
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| Dr. Falk H. Koenemann Aachen, Germany |
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| Email: [log in to unmask] Phone: *49-241-75885 |
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| www.elastic-plastic.de |
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