Rheological modeling. <i>Report by the laureate of the 2023 M.V. Lomonosov Grand Gold Medal of the Russian Academy of Sciences</i>
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Rheological modeling. <i>Report by the laureate of the 2023 M.V. Lomonosov Grand Gold Medal of the Russian Academy of Sciences</i>
Annotation
PII
S0869587324120035-1
Publication type
Article
Status
Published
Authors
H. Altenbach 
Affiliation: Otto von Guericke University of Magdeburg
Pages
1090-1099
Abstract
The article discusses the method of rheological models and the models themselves, as well as modeling of the defining equations based on this method. Some historical information is given, and the method of rheological models proposed by V.A. Palmov is presented. One-dimensional equations are briefly described, three-dimensional equations for isotropic media are considered. It is noted that the method of rheological models for solving two-dimensional problems of continuous media was first applied by the author at the beginning of his scientific activity. In this article, he presents the basic relations for elastic and inelastic plates, and considers an example of complex defining equations for a metal alloy.
Keywords
метод реологических моделей определяющие уравнения механика сплошных сред поведение материалов гипотезы эквивалентности
Received
22.02.2025
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16
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References

1. Giesekus H. Phänomenologische Rheologie. Eine Einführung. Berlin, Heidelberg, New York: Springer, 1994.

2. Tanner R.I. Engineering Rheology. Oxford: Clarendon Press, 1985.

3. Doraiswamy D. The origins of rheology: a short historical excursion // Rheology Bulletin/ 200, vol. 71, no. 1, pp. 7–17.

4. Altenbach H. Kontinuumsmechanik − Eine elementare Einführung in die materialunabhängigen und materialabhängigen Gleichungen, 4. Aufl. Berlin, Heidelberg: Springer, 2018.

5. Christensen R.M. Theory of viscoelasticity − an introduction, 2nd edn. New York et al.: Academic Press, 1982.

6. Рейнер М. Реология. М.: Наука, 1965. Rayner M. Rheology. Moscow: Nauka, 1965. (In Russ.)

7. Krawietz A. Materialtheorie − Mathematische Beschreibung des phänomenologischen thermomechanischen Verhaltens. Berlin, Heidelberg: Springer, 1986.

8. Hutter K., Jöhnk K. Continuum methods of physical modeling-continuum mechanics, dimensional analysis, turbulence. Berlin, Heidelberg: Springer, 2004.

9. Пальмов В.А. Нелинейная механика деформируемых тел. СПб: Изд-во Политехнического университета, 2014. Palmov V.A. Nonlinear mechanics of deformable bodies. St. Petersburg: Publishing House of the Polytechnic University, 2014. (In Russ.)

10. Ruggeri T. Galilean invariance and entropy principle for systems of balance laws // Continuum Mechanics and Thermodynamics. 1989, vol. 1, no. 1, pp. 3–20.

11. Boillat G., Ruggeri T. On the shock structure problem for hyperbolic system of balance laws and convex entropy // Continuum Mechanics and Thermodynamics. 1998, vol. 10, no. 5, pp. 292–295.

12. Müller I., Ruggeri T. Rational Extended Thermodynamics, 2nd edn. New York: Springer, 1998.

13. Müller W.H. An Expedition to Continuum Theory. Dordrecht: Springer, 2014.

14. Müller W.H., Vilchevskaya E.N., Weiss W. Micropolar theory with production of rotational inertia: a farewell to material description // Physical Mesomechanics. 2017, vol. 20, no. 3, pp. 250–262.

15. Altenbach H., Eremeyev V.A. (eds) Generalized continua − from the theory to engineering applications, CISM International Centre for Mechanical Sciences, vol. 541. Vienna: Springer, 2011.

16. Altenbach H., Maugin G.A., Erofeev V. (eds) Mechanics of generalized continua, Advanced Structured Materials, vol. 7. Berlin, Heidelberg: Springer, 2011.

17. Altenbach H., Forest S., Krivtsov A. (eds) Generalized continua as models for materials with multi-scale effects or under multi-field actions, Advanced Structured Materials, vol. 22. Berlin, Heidelberg: Springer, 2013.

18. Eremeyev V.A., Lebedev L.P., Altenbach H. Foundations of Micropolar Mechanics. Springer-Briefs in Applied Sciences and Technology − Continuum Mechanics. Berlin, Heidelberg: Springer, 2013.

19. Blumenauer H. (Hrsg.) Werkstoffprüfung, 6. Aufl. Leipzig, Stuttgart: Deutscher Verlag für Grundstoffindustrie, 1994.

20. Altenbach H., Bolchoun A., Kolupaev V.A. Phenomenological Yield and Failure Criteria // Plasticity of Pressure-Sensitive Materials (ed. by Altenbach H., Öchsner A.). Berlin, Heidelberg: Springer, 2014, pp. 49–152.

21. Kolupaev V.A. Equivalent stress concept for limit state analysis, Advanced Structured Mechanics, vol. 86. Cham: Springer, 2018.

22. Bridgman P.W. The physics of high pressure. London: G. Bell and Sons, 1949.

23. Пальмов В.А. Колебания упруго-пластических тел. M.: Наука, 1976. Palmov V.A. Vibrations of elastic-plastic bodies. M.: Nauka, 1976. (In Russ.)

24. Haupt P. Continuum Mechanics and Theory of Materials, 2nd edn. Berlin, Heidelberg: Springer, 2004.

25. Palmow W.A. Rheologische Modelle für Materialien bei endlichen Deformationen // Technische Mechanik. 1984, vol. 5, no. 4, pp. 20–31.

26. Palmov V.A. Large strains in viscoelastoplasticity // Acta Mechanica. 1997, vol. 125, no. 1, pp.129–139.

27. Трусделл К. Первоначальный курс рациональной механики сплошных сред. М.: Наука, 1975. Trusdell K. The initial course of rational continuum mechanics. M.: Nauka, 1975. (In Russ.)

28. Bruhns O.T. History of plasticity. In: Altenbach H, Öchsner A (eds) Encyclopedia of Continuum Mechanics. Berlin, Heidelberg: Springer, 2020, pp. 1129–1190.

29. Lévy M. Mémoire sur les équations générales des mouvements intérieurs des corps solides ductiles au delà des limites où l’élasticité pourrait les ramener à leur premier état // Comptes rendus de lAcadémie des Sciences. 1870, vol. 70, pp. 1323–1325.

30. von Mises R. Mechanik der festen Körper im plastisch-deformablen Zustand, Nachrichten der Gesellschaft der Wissenschaften Göttingen, Mathematisch-Physikalische Klasse, 1913, pp. 582–592.

31. Prandtl L. Über die Eindringungsfestigkeit (Härte) plastischer Baustoffe und die Festigkeit von Schneiden // ZAMM − Journal of Applied Mathematics and Mechanics // Zeitschrift für Angewandte Mathematik und Mechanik. 1921, vol. 1, no. 1, pp. 15–20.

32. Hencky H. Die Bewegungsgleichungen beim nichtstationären Fließen plastischer Massen // ZAMM − Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 1925, vol. 5, no. 3, pp. 144–146.

33. Hodge P.G., Prager, W. Theorie ideal plastischer Körper. Wien: Springer, 1954.

34. Климов Д.М., Петров А.Г., Георгиевский Д.В. Вязкопластические течения. Динамический хаос, устойчивость, перемешивание. M.: Наука, 2005. Klimov D.M., Petrov A.G., Georgievsky D.V. Viscoplastic flows. Dynamic chaos, stability, mixing. M.: Nauka, 2005. (In Russ.)

35. Bruhns O.T. The Prandtl-Reuss equations revisited // ZAMM − Journal of Applied Mathematics and Mechanics // Zeitschrift für Angewandte Mathematik und Mechanik. 2014, vol. 94, no. 3, pp. 187–222.

36. Shutov A.V., Kreißig R. Finite strain viscoplasticity with nonlinear kinematic hardening: phenomenological modeling and time integration // Computer Methods in Applied Mechanics and Engineering. 2008, vol. 197, no. 2 1, pp. 2015–2029.

37. Bröcker C., Matzenmiller A. An enhanced concept of rheological models to represent nonlinear thermoviscoplasticity and its energy storage behavior // Continuum Mechanics and Thermodynamics. 2013, vol. 25, no. 6, pp. 749–778.

38. Bröcker C., Matzenmiller A. An enhanced concept of rheological models to represent nonlinear thermoviscoplasticity and its energy storage behavior, Part 2: Spatial generalization for small strains // Continuum Mechanics and Thermodynamics. 2015, vol. 27, no. 3, pp. 325–347.

39. Kießling R., Landgraf R., Scherzer R., Ihlemann J. Introducing the concept of directly connected rheological elements by reviewing rheological models at large strains // International Journal of Solids and Structures. 2016, vol. 98, pp. 650–667.

40. Seifert T. Models of cyclic plasticity for low-cycle and thermomechanical fatigue life assessment. In: Altenbach H, Ganczarski A (eds) Advanced Theories for Deformation, Damage and Failure in Materials, CISM international centre for mechanical sciences courses and lectures, vol 605. Springer, 2022, pp. 177–234.

41. Altenbach H. Zur Theorie der inhomogenen Cosserat-Platten // ZAMM − Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Physi k. 1985, vol. 65, no. 12, pp. 638–641.

42. Palmow W.A., Altenbach H. Über eine Cosseratsche Theorie für elastische Platten // Technische Mechanik. 1982, vol. 3, no. 3, pp. 5–9.

43. Альтенбах X. Определение модулей упругости для пластин, изготовленных из неоднородного по толщине анизотропного материала // Механика твёрдого тела. 1987. № 1. С. 139–146. Altenbach X. Determination of elastic modulus for plates made of nonuniform anisotropic material in thickness // Solid state mechanics. 1987, no. 1, pp. 139−146. (In Russ.)

44. Zhilin P.A. Mechanics of deformable directed surfaces // International Journal of Solids and Structures. 1976, vol. 12, no. 9, 10, pp. 635–648.

45. Aßmus M., Eisenträger J., Altenbach H. Projector representation of isotropic linear elastic material laws for directed surfaces // ZAMM − Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 2017, vol. 97, no. 12, pp. 1625–1634.

46. Timoshenko S.,Woinowsky-Krieger S. Theory of Plates and Shells. New York: McGraw-Hill, 1959.

47. Mindlin R.D. Influence of rotatory inertia and shear deformation on flexural motion of isotropic, elastic plates // Journal of Applied Mechanics. 1951, vol. 18, no. 1, pp. 31−38.

48. Альтенбах X. Прямая теория вязкоупругих пластин // Механика твёрдого тела. 1988. № 2. С. 164–169. Altenbach X. Direct theory of viscoelastic plates // Mechanics of a solid body, 1988, no. 2, pp. 16 4−169. (In Russ.)

49. Пальмов В.А. K теории пластин Коссера // Труды ЛПИ. Л.: 1982. Т. 386. С. 3−8. Palmov V.A. K Kosser plate theory // Proceedings of the LPI. L.: 1982, vol. 386, pp. 3−8. (In Russ.)

50. Наумов В.Н., Пальмов В.А. Деформирование жёсткопластических пластин с упрочнением // Труды ЛПИ. Л.: 1982. Т. 386. С. 9−14. Naumov V.N., Palmov V.A. Deformation of rigid plastic plates with hardening // Trudy LPI. L.: 1982, vol. 386, pp. 9−14. (In Russ.)

51. Aßmus M., Altenbach H. On viscoelasticity in the theory of geometrically linear plates // Altenbach H., Öchsner A. (eds) State of the art and future trends in material modeling, Advanced Structured Materials. Cham: Springer International Publishing, 2019, vol. 100, pp. 1–22.

52. Naumenko K., Altenbach H., Kutschke A. A combined model for hardening, softening, and damage processes in advanced heat resistant steels at elevated temperature // International Journal of Damage Mechanics. 2011, vol. 20, no. 4, pp. 578−597.

53. Altenbach H., Girchenko A., Kutschke A., Naumenko K. Creep Behavior Modeling of Polyoxymethylene (POM) Applying Rheological Models // Inelastic Behavior of Materials and Structures Under Monotonic and Cyclic Loading (ed. by Altenbach H., Brünig M.). Cham: Springer, Advanced Structured Materials, 2015, vol. 57, pp. 1–15.

54. Altenbach H., Altenbach J., Kissing W. Mechanics of Composite Structural Elements, 2nd ed., Singapore : Springer, 2018.

55. Eisenträger J., Naumenko K., Altenbach H. Calibration of a phase mixture model for hardening and softening regimes in tempered martensitic steel over wide stress and temperature ranges // Journal of Strain Analysis and Engineering Design. 2018, vol. 53, no. 3, pp. 156–177.

56. Eisenträger J., Naumenko K., Altenbach H. Numerical implementation of a phase mixture model for rate-dependent inelasticity of tempered martensitic steels // Ac ta Mechanica. 2018, vol. 229, no. 7, pp. 3051–3068.

57. Eisenträger J., Naumenko K., Altenbach H. Numerical analysis of a steam turbine rotor subjected to thermo-mechanical cyclic loads // Technische Mechnik. 2019, vol. 19, no. 3, pp. 261–281.

58. Жилин П.А. Рациональная механика сплошных сред. СПб.: Изд-во Политехн. ун-та, 2012. Zhilin P.A. Rational mechanics of continuous media. St. Petersburg: Publishing House of the Polytechnic University. Unita, 2012. (In Russ.)

59. Altenbach H., Altenbach J., Zolochevsky A. Erweiterte Deformationsmodelle und Versagenskriterien der Werkstoffmechanik. Leipzig Stuttgart: Deutscher Verlag für Grundstoffindustrie, 1995.

60. Altenbach H., Bolchoun A., Kolupaev V.A. Phenomenological Yield and Failure Criteria. In: Plasticity of Pressure-Sensitive Materials (ed. by Altenbach H., Öchsner A.). Berlin, Heidelberg: Springer, 2014, pp. 49–152.

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