Ciavarella’s theorem: A story of plagiarism, fraud and forgery!

 J. Jäger, Blattwiesenstr. 7, D-76227 Karlsruhe, Germany, website:

     Dr. Ciavarella’s closure (IJSS, Vol. 38, 2001a, 2459-24623) on my discussions raises some questions, which I would like to address in this summary.  Recently, new publications appeared, in which Ciavarella presented my results under his name with omission of my original papers. It seems, that this problem started with Ciavarella’s priority claim in his second email, in April 98. I expected a rapid end of Ciavarella’s originality claims after he found out that my papers are many years older as his first contributions. To my surprise, Ciavarella decided simply to omit my publications in his references and even today he still continues to republish my formulas and principles under his name. I decided to publish the missing references in two discussions, after I found out that my publications were omitted (with one exception) in Ciavarella’s numerous publications on plane and axisymmetric contact of equal material with friction. It is clear that a complete reference list is necessary for readers of scientific articles, and authors with incomplete  references act unlawful when they attribute other people’s achievement to their own publications. My theory is also much better developed and covers general loading scenarios, torsion, impact and different geometries. The only  exception in Ciavarella’s references was my late paper from 1998 (which was not even published at the time) in a review (Barber, Ciavarella, 2000), where Ciavarella initially wrote that ” ...Ciavarella discovered the Cattaneo-Mindlin generalization...”. In context with my discussions, this formulation was corrected later, and a second paper (Jäger, 1997, Arch. Appl. Mech.) was included in the reference list  (after I contacted Prof. Barber), but my axisymmetric paper from 1995 (Jäger, 1995) was still omitted. Since I am the copyright holder of this principle, the Berne Copyright Convention ( requires the quotation of the first publication and related papers, if necessary.

     It is very well possible that Ciavarella did not read my publications when he started his research (which shows bad research and documentation), but very many people noticed my conference contributions and publications and knew my theory. It is not even necessary that Ciavarella did read my papers, because it was sufficient when he knew the idea. In 1994, I even sent a preprint of my paper on axisymmetric contact to Dr. D. Nowell in Oxford, who works at the department of Prof. Hills. Also, Ciavarella knew one of my papers (Jäger, J, J. Appl. Mech., 1996, Stepwise loading .., Vol. 63, 766-773 ), which contains a reference list of my other articles. Finally, Ciavarella received all my publications in  April 98, but he still omitted them in the revisions of his articles. His argument for the omission was, that Coulomb’s inequalities have not been proved in my papers. Since he published the same formulas, as I showed in the  discussions, this omission alone can very well be regarded as copyright violation, but Ciavarella seems not aware that this is unlawful. I tried to inform publicity with two discussions, which contain the omitted references and improved Ciavarella’s results. In the second discussion, I even showed that Ciavarella’s calculations are unnecessary.

     Not only are publications missing in Ciavarella’s closure (2001a), but the page numbers of most of Cattaneo’s articles are also absent, which is exactly Ciavarella’s style of bad documentation. Even the references of Ciavarella’s own papers are wrong, e. g. the publication by Ciavarella (1998c) did not appear in Vol. 64 of J. Appl. Mech. but in Vol. 65.  Such errors happen frequently in Ciavarella’s papers and the readers may get problems searching the articles and may not find out which sources were used.  Besides, I asked Ciavarella for copies of Cattaneo’s papers in 1998, but he told me that he threw papers away and does not have them any more. It is not easy for me to obtain these copies, because I work in industry and have no access to Italian libraries. Ciavarella still had a chance to acknowledge my results and to improve his method in his closure, but he used it for presentation of his own work, instead. Next, I will address the Coulomb inequality problem.

      The reader can verify that Ciavarella did not calculate the displacements and even used a wrong formula in his publication on 3-D contact, i. e. he did not prove the Coulomb slip condition in his papers, as I mentioned in my first discussion. In his publication on plane contact, Ciavarella presents a formula (eq. 14 in Ciavarella 1998a) for the slip velocity g/t, with the elastic displacement g instead of the slip, i. e. the rigid body term in tangential direction was forgotten.  More errors appeared in equ. (21) of the same paper, where the condition  g/x=g’(x) < 0 was postulated for the displacement in the slip area. First, this condition holds for the slip velocity s/t<0 instead of displacements, and, second, Ciavarella used the derivation with respect to x instead of the time t.  In this context, it should  also be noted that Ciavarella’s theory on 3-dimensional contact always violates Coulomb’s inequality for the slip direction, because it requires Poisson’s number zero, but such materials do not exist. Therefore, Poisson number must be different from zero and would introduce a misalignment between force and displacement. This misalignment, however, was not mentioned in Ciavarella’s article, and his theory remains incomplete. It is wrong when Ciavarella writes  that Cattaneo proved Coulomb’s inequalities, because Cattaneo did not calculate the displacements either and did not mention the mismatch between the slip direction and the frictional traction. This aspect is also missing in  Mindlin’s contribution, but numerical calculations show that the discrepancy amounts to a few degrees only, as long as a stick zone exists (partial slip). During gross slip, however, a redirection of the traction occurs, which must  be considered. Consequently, it can be justified to neglect Coulomb’s inequalities in some cases, because neglection of side effects is the essence of every simplification, as long as the error is small and the theory remains  simple.

     In the discussion, I compared Ciavarella’s results with my earlier work and listed some of my publications, which Ciavarella omitted. Ciavarella’s closure is also appended, although he did not answer the questions, especially my statement that his calculations are unnecessary. His argumentation shows that he did not derive the conclusion that the corrective traction component in the stick zone is the full slip traction of the stick area: q*=fp*, and, thus, did not find the principle, which I use in my papers. The reader should not be confused with Ciavarella’s rejection of my elastic superposition method, which I even regard as more  important than the generalization of Cattaneo. The potential theory in contact mechanics (Boussinesq-Cerruti equations) is a linear superposition of point forces. I regard the rest of Ciavarella’s arguments as a systematic  misinformation and see no reason to treat Ciavarella’s publications as independent contribution. It is characteristic that Ciavarella’s work is restricted to the special case of half-planes and axisymmetric bodies, i. e. the previously published cases, and the 3D paper makes no exception here. I encourage the reader to check Ciavarella’s future publications on this point and to compare them with my original contributions.

      At the beginning of his closure, Ciavarella (2001a) charactarized his papers as “independent overlapping contributions”, which he justified with the confirmation “... that I did not know Dr.  Jäger’s papers ... until April 1998”. Such a misinterpretation of independent working qualifies every person, who does not read scientific papers, to plagiarize publications. In the same sentence, Ciavarella presents it as the same “... as it was at the time of Cattaneo (1938) and Mindlin (1949)”. Here, Ciavarella compares himself with Mindlin, but Mindlin was an authority in mechanics. The name of Mindlin should not be involved in this case, because it is plausible that he did not know Cattaneo’s publication in Italian language in an Italian paper at that time, but Mindlin quoted Cattaneo in a foot-note in his article (1949), and incorporated new solutions on torsion in his paper. Moreover, my contributions appeared in international journals in the English language, and review journals as, “Applied Mechanical Review”, provide a general survey on articles. Besides, as I mentioned earlier, it was not necessary  to know my publications, because the idea propagated much faster and my superposition technique even belongs to the general scientific knowledge in contact mechanics, today. 

      It is also typical that Ciavarella is annoyed with my theory of elastic friction, which ”...Dr. Jäger self-promotes under his name”, but I have no other possibility to defend my principle against  Ciavarella’s method, which Ciavarella calls ”Ciavarella-Jäger theorem”, because the latter destroys the simplicity and obstructs the application to other problems. Moreover, the word theorem is not correct, as I will explain  below, and should be regarded as a forgery of my principle. The reader may keep in mind that elastic friction is not so much a discovery but rather a model with some necessary assumptions and simplifications. The neglection of the slip condition is necessary for general 3-dimensional load cases, as it was explained in Jäger (1996, Stepwise loading of half-spaces ..., J. Appl. Mech., Vol. 63, 766-773), a paper which Ciavarella knows. A correct application of a model and the neglection of unnecessary side effects gives new results, which can be corrected and generalized in future publications.

     I also encourage the reader to pay attention to the marginal  notes, which Ciavarella interweaves in his text, and suggest to learn from it how to avoid such a style, as it may produce a bad impression of the author. It is also bad style to reproduce formulas on axisymmetric contact, which  were published in numerous other papers and already solved in Jäger (1995, Arch. Appl. Mech., Axisymmetric bodies..., Vol. 65, 478-487). Besides, where are the inequalities which belong to Coulomb’s law in equations (1)-(7) of Ciavarella’s closure? Readers may also consider that it should be regarded as copyright violation, when authors republish existing ideas without quotation of original sources, and should pay attention to future publications of such people under the aspect of repetition. Since Ciavarella and others are sceptical about a rigorous proof of Coulomb in my papers, as he writes in his last sentence, the door is open for republication of other papers without quotation of sources, and my copyright is lost! Therefore, I make an appeal to responsible scientists to check reference lists carefully and to publish discussions whenever necessary. Authors have the obligation to answer  discussions when they publish articles, and should not complain as Ciavarella did in his first sentence of the closure. It is first of all a loss of time to republish existing solutions, and readers should not be confused about all  the contradictions in Ciavarella’s closure. How people can avoid all these problems is explained in an interesting note on plagiarism. from John R. Edlund, California State University.

     There is not only a similarity between the formulas in my and Ciavarella’s papers.  Ciavarella even uses my words on the first page of his closure (Ciavarella, 2001a), where he wrote that “At the end of 1996...I noticed that in the derivation of the [generalized] Cattaneo theory ... the solution to Cattaneo’s  problem is a superposition of normal contact solutions”. This formulation was given without reference, and never appeared in Ciavaralla’s publications, before he received all my papers in April 98. Before that date, Ciavarella  always presented an integral equation for the corrective traction q* (examples with reference follow below), and solved this equation by the same method as the normal problem. Thus, he did not find the relation q=f(p- p*),  which I always use in my papers. Moreover, Ciavarella rejected my superposition method for axisymmetric contact on page 2461 of his closure (Ciavarella 2001a), where he wrote that  “ ... it is not a general principle that solutions of contact problems can be superposed ...”. The last sentence explains why Ciavarella did not publish the formulation that the tangential traction is the difference of the normal pressure of the contact and the stick area multiplied with the coefficient of friction, which I use since 1995 exactly as it appears on this web site (publications). As example, Ciavarella  presented an integral equation (eq. 20 in Ciavarella, 1998a) for the corrective traction component q* and wrote that it is “ ... of the same form as the original equation for normal contact ....with p(x) replaced by -q*/f, and the domain of the integral suitably scaled”. It seems that this scaling  process forced Ciavarella to repeat the formulation of the integral equation for q*/f separately for each surface in his examples of the corresponding paper (Ciavarella, 1998b) for a sharp wedge (eq. 8), rounded wedge (eq. 17), flat rounded punch (eq. 24), truncated punch (eq. 34) and all others. Nowhere appears the expression that the traction is a superposition of two normal contact solutions. In the symmetric case, the corrective traction can be written as q*=fp(a*), with the stick radius a* (or half-length in plane contact), and separate equtions are unnecessary.  The scaling factor follows from the tangential force Q , which is of the same form: Q = fP(a)-fP(a*), with the normal force P, or from the tangential displacement. All this proves clearly that Ciavarella is presenting my formulation as his own  result.  

     Ciavarella wrote on page 2460 of his closure (2001a) that “ ... The results of (Ciavarella 1998c) can probably be automatically extended to the general loading case using the arguments of Jäger (1998). The resulting “Ciavarella-Jäger theorem” would be a very powerful tool ... “. Here, the reader should notice that the expression “theorem” appears without reference, whereas Ciavarella   published only a collection of examples for the frictional traction without any theorem in his papers. Thus, the reader must have the impression that Ciavarella refers to the principle for elastic friction published in Jäger (1998).  This principle, however, can not be regarded as a theorem, because Coulomb’s inequality for the slip direction can not generally be proved, especially for three-dimensional loading scenarios. Such a proof is necessary for a theorem in the mathematical sense, in contrast to a principle based on physical properties. Also, a mathematical theorem is not appropriate for a law, which is based on Coulomb friction. Coulomb’s law is a mathematical  simplification for the frictional force as a function of the normal force, under neglection of nonlinearities and additional parameters. Therefore, it can better be formulated as a principle in the sense of a general physical rule, which explains elastic effects in frictional processes for a wide class of problems. Even when the assumptions are not completely satisfied, it can be used as approximation, but never as exact result. 

      Recently, Ciavarella (2001b) published another paper about frictional contact with the following sentence: “A more general solution to the Cattaneo-Mindlin problem for any plane contact problem (not necessarily Hertzian) was given in Ciavarella (1998a,b) proving that the Cattaneo frictional traction distribution

      q(x)=f(p(x)-q*(x))                                             (3.5)

satisfies both equality and inequality conditions, with q*(x) being the normal contact pressure distribution at some smaller value of the normal load. “ When the reader consults the publications (1998a,b), he will find out that equation (3.5) was never published in the form (3.5) in any of Ciavarella’s papers before 1998. In contrast, Ciavarella (1998a) presented the function q*(x) as a corrective shear traction, which has to be found from an integral equation for q*. Ciavarella (1998b) solved  this equation for special examples, as I mentioned above. Therefore, Ciavarella’s formula must be regarded as a copy of the elastic friction principle published in formula (32) in Jäger (1995). Further, the verbal  formulation is a copy of the following expression in one of my papers (Jäger 1997, page 254, after eq. 40): “Tangential traction ...  is always equal to the difference between the actual normal pressure and the normal pressure for a smaller contact area, multiplied by the coefficient of friction”. Since  these publications were not quoted, neither in Ciavarella (2001b) nor in Ciavarella (1998a,b), Ciavarella’s statement is a plagiarism. In context with the Berne Copyright Convention (, all publications by Ciavarella on the generalized Cattaneo-Mindlin theory are a fraud. 



 Barber, JR, Ciavarella, M, 2000, Contact Mechanics, Int. J. Solids Structures, Vol. 37, 29-43. 

Ciavarella, M, 1998a, The generalized Cattaneo partial slip plane contact problem, I-Theory, Int. J. Solids Struct., Vol. 35, 2349-2362. 

Ciavarella, M, 1998b, The generalized Cattaneo partial slip plane contact problem, II-Examples, Int. J. Solids Struct., Vol. 35, 2362-2378. 

 Ciavarella, M, 1998c, Tangential loading of general 3-D contacts, J. Appl. Mech. 64, 998-1003,

Ciavarella, M, 2001a, Closure on “Some comments on recent generalizations of Cattaneo-Mindlin” by J. Jäger, Int J. Solids Structures, Vol. 38, 2459-2463, see: Closureon this web site.

 Ciavarella, M, 2001b, A review of analytical aspects of fretting fatigue, wtih extension to damage parametes, and application to dovetail joints, Int. J. Solids Structures, Vol 38, 1791-1811. .

 Jäger, J, 1998, A new principle in contact mechanics, J. Tribology, 1998, Vol. 120, p.677-683

 Jäger, J, 1997, Half-planes without coupling under contact loading, Arch. Appl. Mech., Vol 67, 247-259.

 Jäger, J, 1996, Stepwise loading of half-spaces in elliptical contact, J. Appl. Mech., Vol. 63, 766-773

Jäger, J., 1995, Axisymmtric bodies in contact under torsion or shift, Arch. Appl. Mech., Vol. 65, 478-487.

 Mindlin, R.D, 1949, Compliance of elastic bodies in contact, J. Appl. Mech., 71, 259-268.