Encyclopedia of Continuum Mechanics

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Huber, Maksymilian Tytus

  • Ryszard B. PęcherskiEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_305-1

Maksymilian Tytus Huber (*4th of January 1872, at Krościenko upon Dunajec in southern part of Poland, which belonged then to the Austro-Hungarian Empire and it was named Galicia; † 9th of December 1950 in Kraków) was a great personality and world-known scientist in the field of mechanics of solids and structures. His scientific interests covered in particular material strength theories, the theory of elastic orthotropic plates, problems of elasticity, and applied mechanics.

https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Maksymilian_Tytus_Huber%2C_portrait.jpg/300px-Maksymilian_Tytus_Huber%2C_portrait.jpg

This biographical note is based mainly on two works (Olesiak 2000; Olesiak and Engel 2006). The first one, directed to the international audience, provides the historical, political, and cultural background of the times of Huber’s activity. From this work that is full of many interesting details, stories, and anecdotes, only certain fragments were used, which are related directly with the most important facts of biography of M.T. Huber. The book (Olesiak and Engel 2006) was helpful in checking the biographical data and providing more actual details related with description of Huber’s academic activity and his scientific legacy.

Family and Education

Maksymilian Tytus Huber was born on the 4th of January 1872 at Krościenko upon Dunajec in southern part of Poland, known at that time Galicia and belonged to the Austro-Hungarian Empire. His father Rudolf was a clerk in the revenue service and his mother Maria, maiden name Rzesińska. He had two younger brothers, Rudolf (*1875–†1942), the known artist photographer living in Lwów, and Kazimierz (*1879–†1948), graduated from Lwów Polytechnic, 1903, in water and sewage engineering; the both brothers and the elder one Maksymilian were the members of Lwów Polytechnic Society. The family changed often the place of residence due to his father’s employment. Therefore, young Huber attended the primary school at Limanowa, secondary school first in Kraków and next at Nowy Sącz, Kołomyja, and finally in Lwów then Lemberg (nowadays, since 1945, Lviv in Ukraine). M.T. Huber graduated from the 4th Gymnasium in Lwów and entered the Faculty of Civil Engineering at Lwów Polytechnic. Already as a student, he showed great ability toward mathematics. His first publication on Simple Construction of Hyperbola appeared in Czasopismo Techniczne, 1890 (Proceedings of Lwów Polytechnic Society). In 1892 he published in Czasopismo Techniczne a paper New Graphical Method of Determination of the Inertia Moments. In 1894 Huber constructed an instrument for drawing the moments of inertia and the first moments of plane figures. In 1895 he graduated and received the diploma as “superbly talented.” After completing his military service, Huber received a 1-year scholarship which let him study at the Berlin University. He studied pure mathematics and astronomy and took part in the seminars of Professor H.A. Schwartz. During the stay in Berlin, M.T. Huber was interested in combinatorics and elliptic functions. In August 1897 he returned in Lwów, and since December he started to work in the State Drainage Office. He worked there for 1 year helping financially in education of his two younger brothers. However, he felt a call to scientific work, and since October 1898 he managed to get the position at the Chair of Mathematics of Lwów Polytechnic. At that time he published a contribution in Wiadomości Matematyczne (Mathematical News). In 1899 he moved to Kraków where he became professor of Theoretical Mechanics in the Industrial College (Wyższa Szkoła Przemysłowa). At the same time, he has not abandoned the research and consequently defended his doctoral thesis on the theory of contact of elastic solids at Lwów Polytechnic in 1904. The thesis entitled Zur Theorie der Berührung fester elastischen Körper was published in Annalen der Physik (Huber 1904a). In the same year, the pivotal paper on Specific Strain Work as a Measure of Material Effort – A Contribution to the Foundation of the Strength of Materials Theory was published in Polish in Czasopismo Techniczne (Huber 1904b). In the footnote it is stated that the present publication contains the author’s paper published in Polish in the current volume Prace matematyczno fizyczne (Transactions of Mathematics and Physics, vol. XV, 1903, Warsaw) and entitled O podstawach teorii wytrzymałości (On foundations of the strength of materials theory). For 1 year Huber taught mathematics on Advanced Courses for Women in Kraków (1905–1906).

Professional Career at Lwów Polytechnic

In 1906 M.T. Huber Dr. Eng. returned again to Lwów, where he was invited to start the courses on the theoretical mechanics. Two years later, on the 1st of October 1908, he was appointed Professor of the Polytechnic and the head of the newly established Chair of the Technical Mechanics. In the same year, he married Maria Łuszczkiewicz. In years 1910–1912, Professor Huber acted as the elected dean of the Civil Engineering Faculty. In 1911 he began organizing the strength of materials laboratory. He was appointed a member of the council at the Vienna Technical Experimental Office, and in 1913 a consultant at the Museum of Industry and Craft in Vienna. In 1914 Professor Huber was elected the rector of the Lwów Polytechnic. In spite of the rector position, he was called up into the army. He took part in the battle by Rohatyn, and later after a long-lasting siege by the Russian Army of the fortress Przemyśl, the whole garrison surrendered on 22nd March of 1915, and he went into captivity. In this way, M.T. Huber as an officer of the Austro-Hungarian Army spent 3 years in Russia as a prisoner of war. In captivity he learned Russian and studied the literature on the achievements in the field of the theoretical and solid body mechanics in Russia. Professor Huber corresponded with S.P. Timoshenko and finally met him at the end of his stay in Russia. He corresponded also with B.G. Galerkin. With the help of the Polish committee in Russia, he was allowed to use the Kazań University Library to carry the research work. After the outbreak of the February revolution in 1917, the change of government and the efforts of Professor W. Orłowski who organized the Polish schools in exile, M.T. Huber was allowed to teach physics in a Polish secondary school. In summer 1918, he returned to Lwów to take over the position as the head of the Chair of the Technical Mechanics at Lwów Polytechnic. Unfortunately, the long period of separation resulted in the breakup of Huber’s marriage. Four years later he married a widow Janina Godlewska, maiden name Dzieślewska (*12th of November 1888, †12th of November 1955). To organize the academia and university education in the first period after World War I, in particular in Poland just reuniting after more than 120 years of partition, was a not easy task. Professor Huber was a charter member (1920) of the Academy of Technological Science in Warsaw and a member of the Lwów Scientific Society. He belonged to many advisory bodies. In 1921 M.T. Huber for the second time was elected the rector of the Lwów Polytechnic. Since 1922 he was the head of the Experimental Station of the Lwów Polytechnic. In 1924 Professor Huber participated in the First International Congress of Applied Mechanics in Delft. During the Congress he met R. von Mises and H. Hencky and Professor August Föppl with whom he was corresponding since 1907. In the Second Congress in Zurich in 1926, he delivered a lecture on the interaction of an elastic plate with ribs. In 1923 he was elected a corresponding member of the Mianowski Fund in Warsaw, in the next year the Vice President of the Lwów Polytechnic Society, in years 1925–1928 the President of the Lwów Branch of the Polish Mathematical Society (PTM), and the President of the First Congress, Lwów, 1927. In the same year, the Senate of the Warsaw Polytechnic offered Professor Huber the position of the head of the Chair of Mechanics II. In this way, since the 1st of April 1928, Professor Huber became a faculty member of the Warsaw Polytechnic. The Lwów Polytechnic Society bestowed on him the honorary membership.

Professorship at Warsaw Polytechnic

As a professor at Warsaw Polytechnic, M.T. Huber could expand and intensify his scientific activity. In Olesiak (2000), pp. S108–S109, the concise list of his new duties is presented. They are summarized below. In 1928 he was elected the President of the Academy of the Technological Sciences, and in February 1929 he was invited to deliver a cycle of lectures at the Zurich Polytechnic. The lectures were based on his original papers on applications of the orthotropic plates (Huber 1929). At the 3rd Congress of Applied Mechanics in Stockholm in 1930, he was elected as a member of the International Congress Committee. M.T. Huber took part also in the Congress of the Society for Testing Materials (Zurich, 1931) and in the Congress of the Bridges and Engineering Structures in Paris (1932) delivering a lecture on flat slab floors. In 1933 Professor Huber was elected the President of the Warsaw Polytechnic Society and nominated the head of the Strength of Materials Laboratory of the Warsaw Polytechnic. In June 1934 he was elected the active member of the Polish Academy of Learning (Polska Akademia Umiejętności, PAU) in Kraków and the deputy director of the 3rd Division (Mathematics and Natural Sciences). In 1934 M.T. Huber became the Vice President of the Mianowski Fund while in 1935 the President of the Civil Engineering Division of the Academy for Technological Sciences in Warsaw. In October 1936 he took part in the International Congress of Bridges and Engineering Structures in Berlin. He visited the laboratories in Munich and Karlsruhe in connection with his works on the problems of rail welding and buckling. Professor Huber took part in the Editorial Committee for Academic Monographs and in the Disciplinary Commission for Professors of the State Colleges. In September 1937 he became the chairman of the Applied Mathematics Section of the 3rd Congress of Polish Mathematical Society (PTM), and he delivered a plenary lecture. He received foreign membership of the Masaryk Academy of Labour in Prague and the membership of three Polish Societies. He was active in the Polish Normalization Committee and in the council for metallurgy and metallography at the Ministry of the Military Affairs. First of all, however, besides the public domestic and international activity, he taught at the Warsaw Polytechnic on different graduate courses. He was the supervisor of two generations of scientists in Poland, working in the fields of the mechanics of deformable bodies. One can mention prominent professors of mechanics: Włodzimierz Burzyński, Wacław Olszak, Robert Szewalski, Zdzisław Gubrynowicz, Zbigniew Brzoska, Bronisław Bukowski, Rajmund Kurowski, Jerzy Leyko, Zbigniew Wasiutyński, and Kazimierz Wolski.

Aviation: One of Huber’s Passions

In the first decade of the twentieth century, the wave of interest in flying machines reached also Lwów. M.T. Huber had series of lectures on flying machines at the Lwów Polytechnic Society and at the Kraków Technological Society. In 1910 he believed that the airplanes were too heavy and were not capable of carrying heavier loads, or many people, in contrary to airships. The society “Aviata” was founded in Lwów in 1909. At the same time, the Association of Aviators with students of the Lwów Polytechnic had been organized. M.T. Huber was its first curator. In 1912 the Association of Aviators announced a contest for a model of the best glider. Professor Huber was the member of jury who decided on the results of the contest on 25th of February 1913. After World War I, M.T. Huber was still involved in aviation. In 1930 his lecture notes Statics of Air Structures appeared. Since 1931 till 1939, he directed the research in the Department of Aeronautics at the Ministry of Military Affairs. In 1949 Professor Huber was appointed to the Scientific Council at the Central Institute of Aviation in Warsaw. The passion for aviation transpires in the name of Huber’s house built at Zakopane in the 1930s that was called villa Śmigło in English Airscrew or Propeller.

The Hardship of World War II

During the German occupation, the secondary schools and academic schools in Poland had been shut down. After the death of the President of J. Mianowski’s Fund (Professor K. Lutostański), M.T. Huber became the acting president until his displacement in August 1944. He succeeded to hide a part of Fund’s property and to complete the Polish edition On Radioactivity by Maria Skłodowska-Curie. He ceased also to cooperate with Zentralblatt für Mechanik. Professor Huber taught in trade schools on clandestine courses and since 1942 in the Higher Technical School. He supervised two habilitation theses by Z. Wasiutyński and by B. Bukowski that were defended within the clandestine polytechnic activity. He concentrated on completing and writing monographs and academic textbooks. Two copies of the manuscript Technological Mechanics of Solid had been destroyed in the fire; however the manuscript The Theory of Elasticity avoided a similar fate. Also the manuscript of Technological Stereomechanics was saved, for it was kept by Dr. Z. Kłębowski outside Warsaw. As a result of the uprising in Warsaw, the Hubers were displaced in August 1944 to the camp at Pruszków near Warsaw. After 2 months of homelessness, they reached their villa Śmigło at Zakopane. A number of Warsaw inhabitants reached Zakopane and in this number a few professors of the Warsaw Polytechnic. A polytechnic in a miniature was formed. They organized “courses of technical drawing” – a clandestine school existing from November 1944 till the liberation of Zakopane on the 29th of January 1945 by the Soviet Army and then acting officially until August 1945. Seventeen students attended the classes (10 students of architecture and 7 students of mechanics). Professor Huber was teaching mathematics, theoretical mechanics, and physics. The remaining subjects were taught by Professor Z. Sochacki from Lwów Polytechnic and Professors R. Śmiałowski, T. Kluz, and W. Dalbor from Warsaw. At Zakopane M.T. Huber was working on re-creation of the lost manuscript on general mechanics. In April and May 1945, he was translating from Russian into Polish a monograph of J.L. Frenkiel Course of the Technological Mechanics Based on Vector and Tensor Analysis (436 pp). The monograph was contemporary for those times and could have had a similar influence on the development of mechanics of continuous media in Poland as S.P. Timoshenko’s Strength of Materials translated also by Huber about 20 years earlier. Unfortunately, the book never appeared. The manuscript of the translation is available in the Archive of the Polish Academy of Sciences. A similar fate met the translation of the Lehrbuch der theoretische Physik (by Georg Joos’, III edition, 1939) that M.T. Huber translated from German into Polish in summer of 1945. The accurate choice of Huber found confirmation in the later English translation that appeared in three editions and several reprints.

Professor Huber Activity in the Postwar Time

At the beginning of May 1945, Dr. S. Turski, one of the organizers of academia in Gdańsk, the town full of severe war damages, made a long trip to Zakopane in order to offer Professor Huber the position of the Rector of Gdańsk Polytechnic, to take over the Chair of Mechanics and to be the head of the Laboratory of Strength of Materials. M.T. Huber did not accept the position of the Rector; however he agreed to come to Gdańsk by September 15 and to take the position of the Head of the Chair and the Laboratory of the Strength of Materials. Professor Huber arrived together with his wife and two of his pupils from Zakopane (H. Jost and C. Puzyna). He was delivering two courses: Technological Stereomechanics and Advanced Problems of Mechanics. Professor Huber preferred this newly introduced term, for stereo in Greek means solid. In his opinion the strength of materials did not correspond fully to the contents of the course because also many other aspects of the behavior of materials and structures were discussed (strains, displacements, elasticity, plasticity, etc.). In Advanced Problems of Mechanics, there were discussed problems of the theory of plates and theory of elasticity, vibrations, and waves. The lecture notes Technological Stereomechanics appeared soon printed by students on duplicating machine. During his stay in Gdańsk, Professor Huber was very active. He taught the students, supervised the PhD theses, was reconstructing the lost in the war manuscripts of his monographs, and wrote tens of research contributions. The title of an Honorary Professor of the Warsaw Polytechnic was conferred upon him on March 28, 1948. He was nominated a member of the Polish delegation on the World Congress of Intellectuals in Wrocław. He did not take part in that event since at the same time he attended the 7th Congress of IUTAM in London. During the Congress he had a chance to meet his old friends, in particular S.P. Timoshenko. In February 1949, Professor Huber left Gdańsk Polytechnic and moved to Kraków, where a special Chair of the Advanced Problems of Mechanics had been created for him, ad personam, with a very small teaching burden. He came back in Gdańsk in October 1949 to receive the doctor honoris causa title. It was his second d.h.c. title. The first one was conferred on him in 1945 by the Mining Academy in Kraków (at present AGH University of Science and Technology). He visited Gdańsk to deliver the general lecture The Theory of Elasticity and Plasticity in the 4th Congress of Polish Civil Engineers held in December 1949. In December he received the national recognition for his scientific achievements, and in 1950 he took part in the organization of the first Congress of Polish Science. In November 1950, the special book devoted to the 50th anniversary of M.T. Huber’s research was published and on the 30th of November 1950 was handed to the Jubilarian by professors W. Nowacki and R. Szewalski. The Jubilee Book contained 22 papers including the paper of M. Roŝ from ETH in Zurich and M.M. Frocht from Illinois Institute of Technology in Chicago. On the 9th of December 1950, Maksymilian Tytus Huber died. His last resting place is in Godlewski’s family tomb at the Rakowicki cemetery in Kraków.

Recognition After the Death

The state funeral gathered many students and his friends, colleagues, and pupils from the whole country. Known scientists sent condolences: C.B. Biezeno, J.M. Burgers, K. Federhoffer, A.M. Freudenthal, K.G. Odquist, M. Roŝ, S.P. Timoshenko, and H. Ziegler. The lecture halls at the technological universities, where Professor Huber taught, bear his name. Also several secondary schools in Poland are named after him. In such towns as Warsaw, Zabrze, and Mikołów, there are streets named after Professor M.T. Huber. In 1960 a tanker, built in Gdańsk shipyard, was named Professor Huber. In 1962 another tanker, built at Gdynia shipyard, was named Prof. M.T. Huber. The Polish Academy of Sciences established in 1953 the Professor M.T. Huber prize for achievements of young scientists in the field of solid body mechanics. In the academia in Poland, as well as at Lviv in Ukraine, a number of sessions, symposia, and conferences were organized to commemorate Professor Huber and his scientific legacy. In 1972, the International Conference on Solid Mechanics was organized by the Institute of Fundamental Technological Research of the Polish Academy of Sciences in Warsaw to celebrate the centenary of Huber’s birth. It took place at Krościenko upon Dunajec, the place of his birth. Another international conference was organized on the occasion of the IUTAM Congress held in Warsaw, August 2004. Since long it was easy to observe that in the coming year 2004, there is the centenary of M.T. Huber criterion. Discussing this question at the beginning of 2002 with Professor Zbigniew S. Olesiak, we came immediately to the conclusion that the connection of these two events would be the great opportunity to pay the tribute to professor Huber and his scientific achievements on the international level. Therefore, we made that before the 21st International Congress of Theoretical and Applied Mechanics, IUTAM, August 15–21, 2004 in Warsaw, within the days 12–14 August, 2004, the International Symposium on Developments in Plasticity and Fracture – Centenary of M.T. Huber Criterion was organized in Kraków in cooperation between the Cracow University of Technology and AGH University of Science and Technology. For both events the Huber’s work was translated and published in Archives of Mechanics (Huber 1904b). The special reprint was distributed among the participants of the Symposium in Kraków and of the IUTAM Congress in Warsaw.

Scientific Achievements

According to the detailed study of Huber’s scientific achievements given in Olesiak (2000) and Olesiak and Engel (2006), one can state that he had written 18 monographs or academic textbooks and over 230 papers. In Olesiak and Engel (2006) there is the complete list of books and articles published by Huber. He elaborated the dictionary of terms used in theoretical mechanics and mechanics of deformable solids in five languages: English, French, German, Russian, and Polish. The dictionary has been published in an enlarged form as a separate book postmortem. Within the books two translations are worth mentioning. The first one is the translation of the book on strength of materials by S.P. Timoshenko that appeared in two editions in 1921 and 1931 and played important role in setting high standard of teaching of this subject in academia. The second one is the translation of the booklet of A. Einstein about the special and general theory of relativity, from the second original edition in German. This translation had also two editions: in 1921 and 1923. The translation was mentioned in the 100th anniversary edition of the booklet, in which in the chapter A History and Survey of Foreign-Language editions, the Polish translation by M.T. Huber is mentioned, and his activity in defending of a new theory is strongly underlined (Einstein 2015):

Among of the strong adherents of relativity was Maksymilian Tytus Huber, a professor of technical mechanics. A Polish Philosopher published an aggressive criticism of Einstein’s theory in the popular press, to which Huber responded with a series of five articles published in the same newspaper explaining and defending Einstein and his theory. Other attacks on relativity prompted Huber to deliver a series of popular lectures, but his most important contribution to the public understanding of Einstein’s theory was his translation of the booklet…. Huber wrote a relatively long introduction…. Huber’s introduction includes a biography of Einstein, but the main emphasis is on the different kinds of objections to the “theory of relativity.” Huber also emphasises the anti-Semitic element of part of the opposition to Einstein and his ideas, both in Germany and in Poland…. Huber concludes his introduction with the following wish: “May the present publication be a good beginning in breaking the ice of naïve prejudices and pseudo-philosophical superposition for the benefit of our scientific culture in the reborn and reunited Fatherland.” He refers to the reunification of Poland after more than 120 years of partition among Austria, Germany and Russia.

Apart from the works on the material strength theories, strength of machines, and bending of orthotropic plates, Huber publications are related with the topics listed below.
  1. 1.

    Monograph Theory of Elasticity in two volumes and papers devoted to the problems of the theory of elasticity and plasticity of structures.

     
  2. 2.

    Problems of buckling and elastic stability as well as buckling of rails.

     
  3. 3.

    The monograph General Mechanics in two editions in 1951 and 1956, the original papers concern problems of vibrations and friction.

     
  4. 4.

    The original works of the structural mechanics and reinforced concrete structures.

     
  5. 5.

    Problems of the mechanical engineering, pipes, and thermal stresses.

     
  6. 6.

    Aviation and mechanics of thin-walled structures.

     
  7. 7.

    Problems related with armaments.

     

The aforementioned list shows that Huber was interested in a variety of problems; however the most known papers deal with material strength hypotheses. His energy-based concept of material effort has a timeless character, which finds confirmation in earlier finding of a great scholar J.C. Maxwell, as well as in the recent studies based on physics of solids, cf., e.g., (Burzyński 2009). As it was stressed in Burzyński (2009), the term “resilience” was used by Maxwell as a measure of material effort understood as elastic energy density of distortion. Independently, Huber (1904b) used simple physical reasoning of molecular interactions to justify the energy hypothesis, in particular, to assume that the density of elastic energy of distortion is a proper measure of material effort. In this way, the pivotal Huber’s concept made the foundations for further studies of Burzyński (2009) on strength criteria for materials revealing strength differential effect (SDE) and energy-based criteria for materials with anisotropic elastic range (Rychlewski 2011; Ostrowska-Maciejewska et al. 2013).

A Great Personality

Maksymilian Tytus Huber was for more than 50 years the highest authority in the fields of general mechanics and mechanics of deformable solids. He was a teacher and master of two, and indirectly of at least three, generations of scientists who played and still play the leading role in academia not only in Poland but also in other countries. For many scholars he is in fact a scientific grandfather. Let us present a longer paragraph worth citing because it was written by one of his students (1945–1948) and assistant (1946–1949) at Gdańsk Polytechnic. Professor Zbigniew S. Olesiak is sharing personal view and feelings about his Master (Olesiak 2000), p. S111:

He possessed a rare ability and willingness to exchange his ideas with many researches, to accept and popularise new ideas. He had excellent relations with mathematicians and physicists. He knew languages: Latin, German, Russian, French, English, probably also Italian, and in his letters I have found also a citation of an Ukrainian proverb. No wonder that he did not have any problems with correspondence. Professor Huber was very systematic, in discussion he was precise and demanded the same from his opponents. His lectures were interesting, he emphasised the logic of derivation of the formulae. …. Professor Huber was a kind man who wanted and liked to help people and to advice, making use of his enormous experience. He never was involved in politics. I can cite a few interesting saying: “without theory technology could not be a branch of learning, it would be just a craft”; “the problems of technology are in fact those of economy”, “experiments are useful only, when they are directed by scientific theory”: …. Professor Huber was fond of good classical music and relaxing reading novels. He liked the music of Bach, Beethoven, Chopin and Franck. He liked fine art and theater. He could not refrain from playing chess, he warned me not to lose too much time from chess. Before World War I he liked to ride on bicycle. He made a trip from Lwów to Gdańsk and back, altogether over 1500 km. Then it was a real feat. The situation in which the country was after the war made him very critical. He had written (on May 5th 1946): “We are assured by radio, that tomorrow, according to the agreement, the Soviet troops will be evacuated from Persia. Therefore, full of hope, I can reply today to your yesterday’s letter.”

References

  1. Burzyński W (2009) Selected passages from Włodzimierz Burzyński’s doctoral dissertation “Study on Material Effort Hypotheses”. Eng Trans 57(3/4):185–215Google Scholar
  2. Einstein A (2015) Relativity. The special & the general theory. 100th anniversary edition. With commentaries and background material by Hanoch Gutfreund & Jürgen Renn. Princeton University Press, Princeton/Oxford, Amazon Kindle e-book editionGoogle Scholar
  3. Huber MT (1904a) Zur Theorie der Berührung fester elastischer Körper. Ann Phys IV:153–163CrossRefGoogle Scholar
  4. Huber MT (1904b) Właściwa praca odkształcenia jako miara wytężenia materyału. Przyczynek do podstaw teorii wytrzymałości, Czasopismo Techniczne, XXII, 1904, Lwów, Organ Towarzystwa Politechnicznego we Lwowie, (Proceedings of Lwów Polytechnic Society). No. 3, February 10, 80–81; No. 4, February 25, 49–50; No. 5, March 10, 61–62; No. 6, March 25, 80–81. Translated from the original in Polish and published in Arch Mech 56, 3, pp. 173–190, Warszawa 2004, Specific work of strain as a measure of material effort. Prof. M.T. HUBER (1872–1950)Google Scholar
  5. Huber MT (1929) Probleme der Statik technisch wichtiger orthotropen Platten. Akademia Nauk Technicznych, Warszawa, p 165Google Scholar
  6. Olesiak ZS (2000) Professor Maksymilian Tytus Huber his life and activity. Eur J Mech A/Solids 19(special issue):S101–S119Google Scholar
  7. Olesiak ZS, Engel ZW (2006) Maksymilian Tytus Huber. Biography and reprints of scientific works (in Polish), Monograficzna seria wydawnicza Biblioteka Polskiej Nauki i Techniki, redaktor naukowy: Adam Mazurkiewicz, Instytut Technologii Eksploatacji – Państwowy Instytut Badawczy w Radomiu, 2006, 2nd supplemented edition 2010Google Scholar
  8. Ostrowska-Maciejewska J, Szeptyński P, Pęcherski RB (2013) Mathematical foundations of limit criteria for anisotropic materials. Arch Metall Mater 58:1223–1235CrossRefGoogle Scholar
  9. Pęcherski RB, Nalepka K, Frąś T, Nowak M (2014) Inelastic flow and failure of metallic solids. Material effort: study across scales. In: Łodygowski T, Rusinek A (eds) Constitutive relations under impact loadings. CISM International Centre for Mechanical Sciences. © CISM, Udine, pp 245–285. https://doi.org/10.1007/978-3-7091-1768-2_6CrossRefGoogle Scholar
  10. Rychlewski J (2011) Elastic energy decomposition and limit criteria. Eng Trans 59 (1):31–63 (translated from the paper in Russian from Adv Mech 7:51–80 (1984))Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Theory of Continuous Media and NanostructuresInstitute of Fundamental Technological Research, Polish Academy of SciencesWarsawPoland

Section editors and affiliations

  • Holm Altenbach
    • 1
  1. 1.Fakultät für Maschinenbau, Institut für MechanikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany