Falk H. Koenemann's blog
https://imechanica.org/blog/11493
enNew theory of elasticity & deformation
https://imechanica.org/node/5014
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
<span>Starting with a few questions which I asked in my introductory class 30 years ago at UC Davis, and which were never answered, I found enough reasons over the years to reject the current theory of elasticity, stress and continuum mechanics entirely. </span>
</p>
<p>
<span>One of the reasons was certainly that my first exposure to deformation was plastic simple shear. For years I searched for a way to understand the structures in shear zones, but did not get anywhere. Just as disconcerting were certain concepts in the theory which I had to accept due to grade pressure, but they were not at all logical to me. At the same time I spent six years studying applied mathematics, but there I had no such difficulties. Eventually it dawned on me that the conventional theory of continuum mechanics (henceforth <strong>CM</strong>) fails systematically and completely for simple shear – energetics, structures, kinematics, brittle, elastic, viscous and plastic. </span>
</p>
<p>
<span>However, asking new questions resulted in the stoniest of silence; if you folks think you are open to discussion, I know better. Just try this one: who proved that strain is a thermodynamic state function? The truth is, the question has never been discussed. The truth is also, strain is not a state function – that is: a term that fully describes the energetic state of the system – but displacement is. But the difference becomes obvious only in the study of deformation with less than orthorhombic properties, that is: simple shear. </span>
</p>
<p>
<span>In 1986 I began to go my own ways, in the fall of 1991 I worked out the theory. Published are now</span>
</p>
<p>
<span><span>(1)<span> </span></span></span><span>Koenemann FH (2001) Cauchy stress in mass distributions. </span><span>Zeitschrift für angewandte Mathematik & Mechanik <strong>81</strong>, suppl.2, pp.S309-S310 (argument fully repeated in #3)</span>
</p>
<p>
<span><span>(2)<span> </span></span></span><span>Koenemann FH (2001) Unorthodox thoughts about deformation, elasticity, and stress. Zeitschrift für Naturforschung <strong>56a</strong>, 794-808</span>
</p>
<p>
<span><span>(3)<span> </span></span></span><span>Koenemann FH (2008) On the systematics of energetic terms in continuum mechanics, and a note on Gibbs (1877). International Journal of Modern Physics B <strong>22</strong>, 4863-4876, DOI 10.1142/S0217979208049078</span>
</p>
<p>
<span><span>(4)<span> </span></span></span><span>Koenemann FH (2008) An approach to deformation theory based on thermodynamic principles. International Journal of Modern Physics B <strong>22</strong>, 2617-2673, DOI 10.1142/S021797920803985X</span>
</p>
<p>
<span><span>(5)<span> </span></span></span><span>Koenemann FH (2008) Linear elasticity and potential theory: a comment on Gurtin (1972). International Journal of Modern Physics B <strong>22</strong>, 5035-5039, DOI 10.1142/S0217979208049224</span>
</p>
<p>
</p>
<p>
<span>Regarding the theory based on Euler & Cauchy, I maintain</span>
</p>
<p>
<span><span>-<span> </span></span></span><span>that the Cauchy stress tensor does not exist; its derivation is flawed because the limit in Cauchy's continuity approach does not exist (1, 3); </span>
</p>
<p>
<span><span>-<span> </span></span></span><span>that the theory of elasticity is profoundly incompatible with the theory of potentials (2, 3), but the latter is the theoretical backbone of all of classical physics; </span>
</p>
<p>
<span><span>-<span> </span></span></span><span>that the form of the First Law of thermodynamics as it is used in CM is in fact an emasculation of the First Law as it is commonly understood; it is invalid, it is not the First Law (3); </span>
</p>
<p>
<span><span>-<span> </span></span></span><span>that the current theory of elasticity is a perpetuum mobile theory: the predicted magnitude of the work done in a volume-neutral deformation is always zero (3); </span>
</p>
<p>
<span><span>-<span> </span></span></span><span>that the current theories of stress and deformation cannot possibly be right because there is no mention of bonds in the theory; hence half the acting forces have been left out of the equilibrium condition (3). </span>
</p>
<p>
<span><span>-<span> </span></span></span><span>For all these reasons, conventional continuum mechanics is not a field theory in the mathematical sense. </span><span> </span>
</p>
<p>
</p>
<p>
<span>It is my firm conviction that the foundations of CM are hopelessly obsolete for at least 150 years. The entire field should have been started all over again after 1847 on the basis of the First Law, because elasticity (and hence stress) is by nature a change of state in the sense of the First Law, and the old concepts by Euler & Cauchy cannot be reconciled with it. To name just one example: it has escaped the community entirely that Clausius (1870) published a law that can reasonably be considered a modern counter proposition to the Navier-Stokes equations, the virial law. Ignoring that law has left CM on a dead track ever since. </span>
</p>
<p>
<span>My theory (4) has nothing in common with the theory used so far. It starts with the First Law. The equation of state </span>
</p>
<p>
<span><span>-<span> </span></span></span><span>is transformed from scalar form into vector form (which is, in fact, Clausius' virial law);</span>
</p>
<p>
<span> </span><span><span>-<span> </span></span></span><span>is generalized to be applicable to all solids, (akin to the theory of Grueneisen 1908); </span>
</p>
<p>
<span><span>-<span> </span></span></span><span>is expanded to consider both work done by normal forces and by shear forces: the work term in scalar thermodynamics is PdV; in my approach, it becomes fdr where f stands for force, and r stands for the radius of the thermodynamic system. </span>
</p>
<p>
<span>My theory makes no a priori assumptions such as "incompressibility" (which does not exist in nature), but volume-constancy is derived as a result. </span>
</p>
<p>
<span>There is a large number of so far enigmatic phenomena for which I believe to have found a solution, especially the properties of elastic and plastic simple shear, including the Poynting effect. At the transition from elastic-reversible to irreversible behavior my approach predicts the existence of a bifurcation: the elastically loaded state is irreversibly relaxed into one of two possible lower states, but they are handed. This bifurcation gives very exactly the orientation of joints, and it is in my eyes an excellent candidate for the origin of turbulence in viscous flow. </span>
</p>
<p>
<span>Since mid-Feb 09 I am aware of a discussion here on iMechanica of my papers eight months ago, but nobody had bothered to let me know. So, to turn up the heat I open this blog. It is high time for public discussion. </span>
</p>
<p>
<span>On my homepage <<a href="www.elastic-plastic.de">www.elastic-plastic.de</a> > are ready for download: preprint PDFs of all papers listed above; links to the journal sites if available; and English translations of Clausius (1870) and Grüneisen (1908). </span><span> </span>
</p>
<p>
<span>Falk H. Koenemann</span>
</p>
<p>
<span>10 March 09</span>
</p>
</div></div></div>Mon, 09 Mar 2009 17:08:57 +0000Falk H. Koenemann5014 at https://imechanica.orghttps://imechanica.org/node/5014#commentshttps://imechanica.org/crss/node/5014