"Christoph Schrank" <[log in to unmask]> schrieb:
> Good morning, everyone,
> if I understood correctly, Dr Koenemann (Discourse 3) criticized that - in case of isochoric, isothermal elastic deformation - Cauchy's stress tensor implies that zero work is done on the body because the volumetric strain (and hence the trace of the stress tensor) is zero. I have a feeling that this apparent problem stems from the fact that much of classical thermodynamics was developed in the context of gases, and in this context, volume work (the pdV-term) seems to be very important as opposed to deviatoric deformation (think of the steam engine). I admit that I am not well-read when it comes to the history of continuum mechanics and thermodynamics, so I apologize in advance for potential misconceptions.
Historically, continuum mechanics is from 1827-1829, thermodynamics
came off the ground 1850-1870, and his matters. Your point that gases
have formed thinking about thermodynamics is correct, but this had no
influence on continuum mechanics which is older. The problem with
continuum mechanics is that it was written
- before people had a clear idea of what a solid is, hence continuum
mechanics does not know about bonds;
- before they had any idea of thermodynamics and the physics of
changes of state, hence the theory still has the conceptual structure
of Newtonian mechanics;
- before they had a clear understanding of mathematical vector spaces,
but continuum mechanics violates its rules massively.
After 1830 this theory has not changed, despite all the new ideas
1850-1870 in mathematics and physics. This theory is not just
maladjusted, it is wrong.
> But as far as I understand the textbooks as non-physicist, there is no problem with the thermodynamics of elasticity and Cauchy's stress tensor.
I am afraid there are plenty of problems. Continuum mechanics has the
conceptual structure of Newtonian mechanics, but it belongs rightfully
into thermodynamics; this means that the two most basic energy
conservation laws we know are mixed up. This is a fatal error.
| Dr. Falk H. Koenemann Aachen, Germany |
| Email: [log in to unmask] Phone: *49-241-75885 |
| www.elastic-plastic.de |