Mechanothermodynamics

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Mechanothermodynamics (MTD) is a section of physics created at the junction of mechanics and thermodynamics,[1][2][3][4][5] in which irreversible transformations of states and consequently, the properties and functions of mechanothermodynamic systems (MTD-systems) under the influence of forces (fields) of different nature – mechanical, thermodynamic, etc. The MTD-system is a thermodynamic medium with discrete volumes of solid moving and deformable bodies (objects, elements, particles, etc.) distributed in it. Bodies can interact both with each other and with the environment.

Etymology[edit]

The term mechanothermodynamics is composed of two English words: mechanics and thermodynamics. Proposed in.[6]

History[edit]

Each scientific discipline has its own subject for study. Figure 1 shows a simplified diagram of the development of some sections of mechanics: from simple to complex. The history of the development of the indicated in Figure 1 and other sections of mechanics is described in the literature (see, for example[4][7][8][9][10][11][12]).

Figure 1 – Simplified hierarchical structure of some objects studied in mechanics: from simple to complex

Attempts to combine mechanics and thermodynamics were unsuccessful for a long time. This is due not so much to the complexity of the problem as to the cardinal differences in the methodology of these two branches of physics.[13][14] So, if thermodynamic processes are irreversible, then the laws of dynamics, on the contrary, are reversible. This means, for example, that thermodynamics poses and solves the problem of describing the evolution of systems from the past to the future, and in the equations of mechanics, replacing the sign (–t) by (+t) gives the same result, i.e. mechanics does not distinguish between past and future.[15] That is why from the standpoint of mechanics it is not possible to develop a theory of the evolution of the material world,[14] while from the standpoint of thermodynamics it is formulated in its most general form: the entropy of the Universe tends to a maximum.[16] On the other hand, mechanics can quantitatively describe the laws governing the motion of any bodies, while in thermodynamics such problems are not even posed.

Since the concept of irreversibility in thermodynamics turned out to be fundamental,[17] it had to be developed in mechanics.[18][19][20][21] In tribo-fatigue,[22][23][24] created at the junction of tribology and fatigue strength, the concept of irreversible damage (ωΣ) of tribo-fatigue systems and their elements is proposed. Thus, with the simultaneous action of contact (during friction) and cyclic volumetric (tensile-compression, bending, torsion, etc.) loads, complex wear-fatigue damages are formed, the evolution of which leads to the achievement of the system (or its elements) of various limiting states (fatigue breakage, wear limit, critical density of chipping pits, etc.). By analogy with thermodynamics, the concept of tribo-fatigue entropy is proposed in tribo-fatigue.[25] But if the thermodynamic entropy STD is a characteristic of energy dissipation,[13] then the tribo-fatigue entropy STF (ωΣ(Ueff)), on the contrary, is a characteristic of energy absorption (UΣeff).[25] And MTD-entropy is formed[5][26] as a combination of two components: SMTD(STD, STF).

Thus, tribo-fatigue became a methodological intermediary between mechanics and thermodynamics (Figure 2), which led to the creation of a new branch of physics. And directly the unification of mechanics and thermodynamics is interpreted in Figure 2 as unrealizable, and therefore the weak connection between them is shown by vertical lines, which are formed by points.[1][4][26]

Figure 2 – Mechanothermodynamics as a branch of Physics

The fundamentals of mechanothermoinamics were developed by L. A. Sosnovskiy and S. S. Sherbakov.[1][2][4][5][26]

Principles of mechanothermodynamics[edit]

To date, four principles of MTD have been formulated,[1][3][4] and their analysis and development have yielded a number of interdisciplinary and transdisciplinary results.[1][2][3][4][5][7][8][6][26] Some of them are described below.

The first principle of MTD: the damageability of everything that exists has no conceivable boundaries: ωΣ(Ueff)→∞.[1][3] This principle states that for the evolution of any system, a unidirectional process of its irreversible damage (ωΣ) and, ultimately, decomposition into infinitely small particles is inevitable. In essence, this is tantamount to the idea that damageability is a fundamental property and an obligatory function of all systems, including living and intelligent systems.[2][4][27]

The second principle of MTD: the fluxes of effective energy Uωeff (entropy Si), caused by sources of different nature, are non-additive and interact with each other in time.[1][26][28][29] The principle indicates the driving force and the main reason for the emergence and development of the internal damageability of the MTD-system – these are dialectic Λ-interactions of the effective energy components in the absorbing medium. Such interaction functions should take three classes of values (Λ>1, Λ<1, Λ=1) in order to reflect not only unity and struggle, but also the direction of the processes of physical hardening (Λ<1)–softening (Λ>1) in the system. Since hardening is always finite, while the intensity of softening can be infinitely high, the interaction of such processes inevitably leads the MTD-system to critical and limiting damage states.[1][5][26]

The third principle of MTD: the development of processes of irreversible damage is possible and is realized with a certain probability P>0, when a finite region with a nonzero level of effective energy (internal entropy) appears in the MTD-system – a dangerous volume VPγ(Uωeff(Si))>0.[2][4][26] If VPγ=0, the MTD-system is stable and its damageability evolution is impossible.

This principle makes it possible to establish the absolute value of the scale (dimensions) of the damage space of the MTD-system. In the general case, many different dangerous volumes are found in it, since their number is due to many loads of a different nature (mechanical, thermodynamic, electrochemical, etc.) and, consequently, many and different criteria for the transition to a dangerous state.[22][26] Separate dangerous volumes can have different sizes and, being combined, interact with each other when loads and / or time changes.[19] The scale of damage to the MTD-system fully characterizes the danger (or risk) of its functioning.[6] Achievement of the critical value of the dangerous volume can generate a flow of nonstationarities in the system, for example, vibration, beatings, the troppy effect.[30][31]

The fourth principle of MTD: motion generates information in the MTD-system if its damage index is nonzero (ωj>0); information turns out to be positive (+ΔI) when the system is strengthened, or negative (–ΔI) when it is weakened. The relationship between movement, damage and information is given by reciprocity relations.[8][32][33]

This principle establishes that the sources of information in Nature are matter and its various damages during movement.[33] External forces and internal interactions are the causes of movement and damage to material bodies and any systems that consist of them. Their long-term action determines the corresponding accumulation of information. An abrupt growth of information is possible at critical points of development, when the amount of accumulated information becomes critical. Any leap of information means a change in its quality.[27]

Evolution of systems[edit]

Based on the first and second principles of MTD, the evolution of systems is described in two ways: either traditionally, using the concept of entropy, or in terms of damage states.[27]

The entropy approach to describing the evolution of systems leads to the law of increasing entropy, written in the simplest analytical form[4][5]

Mtd f 1.jpg

Here, the subscript (TD) means thermodynamic, the subscript (TF) means tribo-fatigue entropy, and the subscript (MTD) means mechanothermodynamic entropy.

Analysis of the evolution of systems in accordance with the law of increasing entropy is shown in Figure 3.

Figure 3 – Evolution of thermodynamic (STD) or mechanothermodynamic (STD ↔ STF) state of the system (А1, А2): a – oscillatory and asymptotic converging processes; b – oscillatory and asymptotic divergent processes

According to Figure 3, thermodynamic (STD) entropy tends to a maximum – for both converging (divergence divF(•)<0) and diverging (divF(•)>0) processes of motion of points (A1, A2) of the system. And mechanothermodynamic entropy (SMTD) does not have such a pattern (other things being the same), since it obeys the law of increase.

Taking the first principle of MTD for the analysis of evolution, the law of a steady increase in the damageability of systems is written in the following form

Mtd f 2.jpg

The law states that the evolution of any system is characterized and inevitable by a sequential process of its irreversible damage (ωΣ) and, ultimately, decomposition into an infinitely large number of small (determined by size dω*) components (fragments, atoms, elementary particles, etc.). In essence, this is tantamount to the recognition of the thesis about the endlessness of evolution, if we take into account that the products of the decay of any system become the building material for new systems. Thus, regardless of the conditions and characteristics of the existence of specific systems, the source (beginning) and the end of them are the same – this is matter. Therefore, matter is one past, present and future of everything. In other words, our Universe is indestructible, since it is material and evolves in terms of damage. This corresponds to the philosophical notion that matter and motion are eternal, and the MTD notion that damageability is a fundamental property and an obligatory function of any systems and objects that make up them.

The complex of irreversible damage (ωΣ) is determined by the effective (absorbed in the system) energy (UΣeff) due to loads of any nature:

Mtd f 3.jpg

Here, the indices n and τ indicate normal and shear mechanical loads, T and Ch – for thermal and electrochemical loads that generate the corresponding energy flows, and U0 is the activation energy of a given substance.[34] The value of U0 approximately coincides with the heat of sublimation for metals and crystals with ionic bonds, as well as the energy of thermal destruction for polymers[35]

Thus, the complex of irreversible damage ωΣ is considered as having an energy content.

A quantitative analysis of the damageability of systems is given in Table 1.[2][4][27]

Mtd t 1-0.jpg

As can be seen, in quantitative terms, the analysis of changes in the states of systems by damage is more informative than, for example, the study of their energy or entropy states, since any damage is real, while the material carriers of energy or entropy are unknown or completely absent.[36] However, the use of the fundamental concepts of energy and entropy is very effective in science, since they underlie many physical laws, for example, universal conservation laws. In this regard, the analysis of the energy and entropy states of systems turns out to be undoubtedly fruitful.

Λ-interactions[edit]

The interaction rule of irreversible damage caused by loads of different nature is written as follows

Mtd f 4.jpg

Similarly, the rule for the interaction of entropy components

Mtd f 5.jpg

The methods for determining the parameters Λ are described, for example, in.[3][26]

These rules allow solving problems of analysis and synthesis, for example, damage in an MTD-system. Analysis: the whole (ωΣ) is broken down into discrete measures of damage, the study of which is useful under appropriate operating conditions. Synthesis: knowing the individual measures of damage, an assessment of the complex (ωΣ) damage of the MTD-system is given. Synthesis is more important than analysis: who knows the whole, he knows everything (Aristotle). Thus, it is established that for Λ>1 the system spontaneously softens, for Λ<1 the system spontaneously strengthens, and for Λ=1 it turns out to be stable. Knowledge of these conditions opens the way to managing the reliability of an MTD-system under certain operating conditions.[4][26]

Combined spatial stress state[edit]

The design diagram of the simplest MTD-system is shown in Figure 4.

Figure 4 – Scheme of the elementary MTD-system

The mechanical and mathematical model of the combined stress state has the form

Mtd f 6.jpg

where σij(V)=σij(M, N, Q), and the indices V, W and T correspond to volumetric, contact and thermodynamic loads; M, N, Q – internal moments, longitudinal and transverse forces (see Figure 4).

The model makes it possible to analyze not only the level (σij) of the combined stress state in the MTD-system, but also the influence of any of the acting loads on the change in the stress state of its elements (such as, for example, direct and back effects in tribo-fatigue[22][23][24]).

Condition of volumetric damage[edit]

In accordance with the third principle of MTD, the mechanical-mathematical model of volumetric damage has the form

Mtd f 7.jpg

If VPγ = 0, the damage evolution of the object is impossible. Here VPγ < V is the absolute value (measure) of the spatial damage of the MTD-system (V is its working (geometric) volume). Calculation methods and classification of dangerous volumes (VPγ) for typical material objects (deformable solids) in various conditions have been developed (see, for example[22][26]).

In the general case, a set of {VPγ} dangerous volumes is found in the system, since their number is due to many loads of a different nature (mechanical, thermodynamic, electrochemical, etc.) and, consequently, many and different criteria for the transition to a dangerous state. Individual dangerous volumes can be of any size and, being combined, dialectically interact with each other when the loads and / or time change. In this regard, the patterns of evolution of organic and inorganic systems can be studied at the appropriate scale levels.

A particular example of the implementation of multiple damageability of a deformable system is given in Figure 5: a number of dangerous volumes are visualized on the graphs.

Figure 5 – Sections of dangerous volumes Vij in the roller / shaft system

Multi-criteria limiting state[edit]

In accordance with the third principle of MTD, the physical and mathematical model of the multicriteria limiting state in terms of relative damage has the form

Mtd f 8.jpg

Based on this model, a particular formula was obtained for the temperature dependence of the limiting stresses

Mtd f 9.jpg

Three criteria of condition are summarized here: T, σu, σ−1. Experimental verification of this formula was made based on the results of more than 600 tests and is given in Figure 6.

Figure 6 – Experimentally substantiated MTD-function of critical damageability (tensile strength, endurance limits) states for metals and polymers (indicated by points of different configuration)

A feature of the predictive equation is that the temperature dependence of ultimate stresses is adequately described by a single equation in the temperature range from 3K to 0.8TS, where TS is the melting point (in Figure 6). According to this equation, the ultimate stress increases in proportion to the complex parameter CT, depending on the test conditions for samples of different sizes (from 0.5 to 16 mm in Figure 6).

Intervals I, II, III, IV correspond to the properties of low-strength, strong, high-strength and ultra-high-strength materials and their states.

Comprehensive calculation of MTD-systems[edit]

The calculation scheme for MTD-systems is shown in Figure 7. According to this figure, when designing MTD-systems, it is taken into account: design and technology (VPγ/V0, SPγ/S0, Θtech/Θn), materials and time (mj, j=1, 2,…, t), damage (from contact load ωτ, from cyclic load ωσ, from thermal load ωT, from electrochemical load ωch), conditions of damage interaction (Λσ/τ, ΛT\M, Dσ,τ,T).

Figure 7 – Main channels of MTD-system resource management

References[edit]

  1. ^ Jump up to: a b c d e f g h Sosnovskiy, L. A., Sherbakov, S. S. Mechanothermodynamics. – Springer, 2016. – 155 p.
  2. ^ Jump up to: a b c d e f Sosnovskiy, L. A., Sherbakov, S. S. Mechanothermodynamical System and Its Behavior // Continuum Mechanics and Thermodynamics. – 2012. – № 24. – Р. 239–256.
  3. ^ Jump up to: a b c d e Sosnovskiy, L. А., Sherbakov, S. S. Principles of Mechanothermodynamics. – Gomel : BelSUT, 2013. – 150 p. (in Russian).
  4. ^ Jump up to: a b c d e f g h i j k Sosnovskiy, L. A. Mechanothermodynamics (about combining great competitors: 1850-2015) // Mechanics of machines, mechanisms and materials. – 2016. – № 4 (37). – P. 19–41. (in Russian).
  5. ^ Jump up to: a b c d e f Sosnovskiy, L. A., Sherbakov, S. S. Mechanothermodynamic Entropy and Analysis of Damage State of Complex Systems // Entropy. – 2016. – Mode of Access : http://www.mdpi.com/1099-4300/18/7/268/htm. – Date of Access : 20.07.2016.
  6. ^ Jump up to: a b c Sosnovskiy, L. A. L-risk (mechanothermodynamics of irreversible damages). – Gomel : BelSUT, 2004. – 317 p. (in Russian).
  7. ^ Jump up to: a b Sosnovskiy, L. A., Sherbakov, S. S. On the possibility of constructing mechanothermodynamics // Science and innovations. – 2008. – № 2 (60). – P. 24–29. (in Russian).
  8. ^ Jump up to: a b c Sosnovskiy, L. A., Sherbakov, S. S. Surprises of Tribo-Fatigue. – Magic Book, 2009. – 200 p.
  9. ^ Buchwald, Jed Z. and Robert Fox, eds. The Oxford Handbook of the History of Physics. 2014. – 976 p.
  10. ^ Timoshenko, S. P. History of the Science of Strength of Materials. 2nd ed. – M. : URSS, 2006. – 536 p. (in Russian).
  11. ^ Dowson, Duncan. History of Tribology. – John Wiley & Sons, 1999. – 768 p.
  12. ^ Suresh, S. Fatigue of Materials. – Cambridge University Press, 2004.
  13. ^ Jump up to: a b Kondepudi, D., Prigogine, I. Modern Thermodynamics (From Heat Engines to Dissipative Structures). – John Wiley & Sons, 1998. – 486 p.
  14. ^ Jump up to: a b John R. Taylor. Classical Mechanics. 2005. – 786 p.
  15. ^ Nicolis, G., Prigogine, I. Exploring Complexity (An Introduction). – New York : Freeman & Company, 2003.
  16. ^ Clausis, R. Mechanical Theory of Heat. – London : John van Voorst, 1867.
  17. ^ Peter V. Coveney. The Second Law of Thermodynamics: Entropy, Irreversibility and Dynamics // Nature. – 1988. – Vol. 333. – P. 409–415.
  18. ^ Handbook of Damage Mechanics. – Springer, 2015.
  19. ^ Jump up to: a b Sosnovskiy, L. A. Mechanics of wear-fatigue damage. – Gomel : BelSUT, 2007. – 434 p. (in Russian).
  20. ^ Kachanov, L. M. Introduction to continuum damage mechanics. – Springer, 1986. – 135 p.
  21. ^ Rabotnov, Yu. N. Elements of Hereditary Solid Mechanics. – Moscow : Mir Publishers, 1980. – 387 p.
  22. ^ Jump up to: a b c d Sherbakov, S. S., Sosnovskiy, L. A. Mechanics of tribo-fatigue systems. – Minsk : BSU, 2010. – 407 р. (in Russian).
  23. ^ Jump up to: a b 摩擦疲劳学 磨损 – 疲劳损伤及其预测. L. A. 索斯洛夫斯基著, 高万振译 – 中国矿业大学出版社, 2013. – 324 p. (in Chinese).
  24. ^ Jump up to: a b Sosnovskiy, L. А., Zhuravkov, М. А., Sherbakov, S. S. Fundamental and applied tasks of Tribo-Fatigue: lectures. – Minsk : BSU, 2010. – 488 p. (in Russian).
  25. ^ Jump up to: a b Sosnovskiy, L. A. On one type of entropy as a measure of energy absorption spent on damage production in a mechanothermodynamic system // Reports of the National Academy of Sciences of Belarus. – 2007. – V. 51. – № 6. – P. 100–104. (in Russian).
  26. ^ Jump up to: a b c d e f g h i j k Sosnovskiy, L. A., Sherbakov, S. S. On the Development of Mechanothermodynamics as a New Branch of Physics // Entropy. – 2019. – №21. – С.1–49.
  27. ^ Jump up to: a b c d Sosnovskiy, L. А., Sherbakov, S. S., Lazarevich, А. А. Fundamentals of the theory of the evolution of inorganic and organic systems, the number of living and reasonable // National philosophy in a global world : proc. of the First Belarusian Congress of Philosophy, Minsk, Oct. 18–20, 2017. – Minsk : Belarusian science, 2018. – P. 155–178. (in Russian).
  28. ^ Frolov, K. V., Makhutov, N. A., Sosnovskiy, L. A. Theory of interaction of irreversible damage // Proceedings of the V International Symposium on Tribo-Fatigue (ISTF 2005) / Ed. by A. P. Khomenko. – Irkutsk–Bratsk, 2005. – P. 10–28. (in Russian).
  29. ^ Zhuravkov, M. A., Sherbakov, S. S., Makhutov, N. A., Sosnovskiy, L. A. On the methodology of phenomenological analysis in mechanics // Theoretical and Applied Mechanics. – 2014. – V. 31. – P. 3–10. (in Russian).
  30. ^ Sosnovskiy, L. A., Sherbakov, S. S. Vibro-Impact in Rolling Contact // Journal of Sound and Vibration. – 2007. – № 308. – P. 489–503.
  31. ^ Sosnovskiy, L. A., Sherbakov, S. S. Troppy Phenomenon (CM104). – Proceedings of 7th International Conference on Contact Mechanics and Wear of Rail / Wheel Systems (Brisbane, Australia, Sept. 24–27, 2006). – Brisbane. – 2006. – V. 1. – P. 115–125.
  32. ^ Sosnovskiy, L. A. On one method of constructing the relationship of movement, information and damage in a mechanothermodynamic system // Mechanics of machines, mechanisms and materials. – 2011. – № 4 (17). – P. 87–90. (in Russian).
  33. ^ Jump up to: a b Sosnovskiy, L. A. Tribo-Fatigue: the dialectics of life. – Ed. 2nd. – Gomel : BelSUT, 1999. – 116 p. (in Russian).
  34. ^ Zhurkov, S. N. Dilaton mechanism of solid strength // Physics of strength and plasticity. – L.: Nauka, 1986. – P. 5–11. (in Russian).
  35. ^ Gabar, I. G. Thermoactivation analysis of the destruction of OCK- and GCK-metals and the concept of the relationship between the parameters of the fatigue curve // Strength of materials. – 1989. – № 11. – P. 61–64. (in Russian).
  36. ^ Feynman, R. Feynman’s Lectures on Physics. – Moscow : Mir, 1963 (in Russian).
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