Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Continuum Mechanics and Thermodynamics
Erschienen in: Continuum Mechanics and Thermodynamics 4/2021

04.05.2021 | Original Article

A new approach to solving the solid mechanics problems with matter supply

verfasst von: Elena A. Ivanova, Luis Eduardo Jatar Montaño

Erschienen in: Continuum Mechanics and Thermodynamics | Ausgabe 4/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We discuss some aspects of using the spatial description and the finite volume method as applied to the solid mechanics problems. The main objective is to study the differential equation relating the strain measure to the velocity gradient. We show that this equation can be reduced to an integral form and the obtained equation has the structure of the balance equation without a source term. On the one hand, such form of equation for the strain measure is convenient when dynamical problems of solid mechanics are solved by using the finite volume method. On the other hand, the balance equation allows us to look at the strain measure as a parameter of state in a broader sense, not as the purely geometrical characteristic. We believe that this interpretation of the strain measure may open up new prospects for describing the processes connected with the substance supply into solids. In order to solve such problems, we suggest to add a source term into the balance equation for the strain measure. We discuss this idea from different points of view. We also solve some problems where the stress–strain state of solids is caused by the source terms in the balance equation for the strain measure.
Vorheriger Artikel Modularity of the displacement coefficients and complete plate theories in the framework of the consistent-approximation approach
Nächster Artikel Negative-stiffness composite systems and their coupled-field properties

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Malvern, E.: Introduction to the Mechanics of a Continuous Medium. Prentice-Hall Inc, Englewood Cliffs (1969)
2.
Truesdell, C.: A First Course in Rational Continuum Mechanics. The John Hopkins University, Maryland, Baltimore (1972)
3.
Eringen, C.: Mechanics of Continua. Robert E. Krieger Publishing Company, Huntington (1980)MATH
4.
Batchelor, G.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (1970)
5.
Loitsyansky, L.G.: Fluid Mechanics. Nauka, Moscow (1987).. ((In Russian))
6.
Daily, J., Harleman, D.: Fluid Dynamics. Addison-Wesley, Massachusetts (1966)MATH
7.
Arienti, M., Hung, P., Morano, E., Shepherd, J.E.: A level set approach to Eulerian–Lagrangian coupling. J. Comput. Phys. 185, 213–251 (2003)ADSMATHCrossRef
8.
Donea, J., Giuliani, S., Halleux, J.P.: An arbitrary Lagrangian–Eulerian finite element method for transient dynamic fluidstructure interaction. Comput. Method. Appl. Mech. 33, 689–723 (1982)MATHCrossRef
9.
Hirt, C.W., Amsden, A.A., Cook, J.L.: An arbitraty Lagrangian–Eulerian computing method for all flow speeds. J. Comput. Phys. 14, 227–253 (1974)ADSMATHCrossRef
10.
McGurn, M.T., Ruggirello, K.P., DesJardin, P.E.: An Eulerian–Lagrangian moving inmersed interface method for simulation burning solids. J. Comput. Phys. 241, 364–387 (2013)ADSMathSciNetMATHCrossRef
11.
Surana, K.S., Blackwell, B., Powell, M., Reddy, J.N.: Mathematical models for fluid–solid interaction and their numerical solutions. J. Fluid. Struct. 50, 184–216 (2014)ADSCrossRef
12.
Brazgina, O.V., Ivanova, E.A., Vilchevskaya, E.N.: Saturated porous continua in the frame of hybrid description. Contin. Mech. Thermodyn. 28(5), 1553–1581 (2016)ADSMathSciNetMATHCrossRef
13.
Pietraszkiewicz, W., Eremeyev, V.A.: On natural strain measures of the non-linear micropolar continuum. Int. J. Solids Struct. 46(3–4), 774–787 (2009)MathSciNetMATHCrossRef
14.
Chung, T.: Computational Fluid Dynamics. Cambridge University Press, Cambridge (2012)
15.
Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method for Solid and Structural Analysis. ElSevier, Netherlands (2005)MATH
16.
Chandrupatla, T.R., Belegundu, A.D.: Introduction to Finite Elements in Engineering. Prentice Hall, United States (2002)MATH
17.
18.
Bowen, R.M.: Theory of Mixtures, Part I. Continuum Physics. III. Ed. A.C. Eringen. Academic Press, New York (1976)
19.
Miller, G.H., Colella, P.: A conservative three-dimensional Eulerian method for coupled fluid-solid shock capturing. J. Comput. Phys. 183(1), 26–82 (2002)ADSMathSciNetMATHCrossRef
20.
Benson, D.J., Okazawa, S.: Contact in a multimaterial Eulerian finite element fomulation. Comput. Methods Appl. Mech. Eng. 193, 4277–4298 (2004)ADSMATHCrossRef
21.
Al-Athel, K.S., Gadala, M.S.: Eulerian volume of solid (VOS) approach in solid mechanics and metal forming. Comput. Methods Appl. Mech. Eng. 200(25–28), 2145–2159 (2011)ADSMathSciNetMATHCrossRef
22.
Schoch, S., Nordin-Bates, K., Nikiforakis, N.: An Eulerian algorithm for coupled simulations of elastoplastic-solids and condensed-phase explosives. J. Comput. Phys. 252, 163–194 (2013)ADSMathSciNetMATHCrossRef
23.
Ortega, A.L., Lombardini, M., Pullin, D.I., Meiron, D.I.: Numerical simulation of elastic–plastic solid mechanics using an Eulerian stretch tensor approach and HLLD Riemann solver. J. Comput. Phys. 257, 414–441 (2014)ADSMathSciNetMATHCrossRef
24.
Ivanova, E.A., Matias, D.V., Stepanov, M.D.: Employment of Eulerian, Lagrangian, and Arbitrary Lagrangian–Eulerian decription for crack opening problem. Mater. Phys. Mech. 42, 470–483 (2019)
25.
Altenbach, H., Naumenko, K., Zhilin, P.A.: A micro-polar theory for binary media with application to phase-transitional flow of fiber suspensions. Contin. Mech. Thermodyn. 15(6), 539–570 (2003)ADSMathSciNetMATHCrossRef
26.
Zhilin, P.A.: Advanced Problems in Mechanics, vol. 1. Institute for Problems in Mechanical Engineering, St. Petersburg (2006).. ((In Russian))
27.
Zhilin, P.A.: Advanced Problems in Mechanics, vol. 2. Institute for Problems in Mechanical Engineering, St. Petersburg (2006)
28.
Zhilin, P.A.: Rational Continuum Mechanics. Polytechnic University Publishing House, St. Petersburg (2012).. ((In Russian))
29.
30.
Müller, W.H., Vilchevskaya, E.N., Weiss, W.: Micropolar theory with production of rotational inertia: a farewell to material description. Phys. Mesomech. 20(3), 250–262 (2017)CrossRef
31.
Vilchevskaya, E.N.: On micropolar theory with inertia production. In: Altenbach, H., Öchsner, A. (eds.) State of the Art and Future Trends in Material Modeling, pp. 421–442. Springer, Berlin (2019)CrossRef
32.
Ivanova, E.A.: On a micropolar continuum approach to some problems of thermo- and electrodynamics. Acta Mech. 230, 1685–1715 (2019)MathSciNetMATHCrossRef
33.
Ivanova, E.A.: Derivation of theory of thermoviscoelasticity by means of two-component medium. Acta Mech. 215, 261–286 (2010)MATHCrossRef
34.
Ivanova, E.A.: Description of mechanism of thermal conduction and internal damping by means of two-component Cosserat continuum. Acta Mech. 225, 757–795 (2014)MathSciNetMATHCrossRef
35.
36.
Ivanova, E.A.: Description of nonlinear thermal effects by means of a two-component Cosserat continuum. Acta Mech. 228, 2299–2346 (2017)MathSciNetMATHCrossRef
37.
Walter, J.: Eulerian Front Tracking for solid dynamics. Los Alamos National Research Laboratory, United States (1999)
38.
Ivanova, E.A., Vilchevskaya, E.N., Müller, W.H.: Time derivatives in material and spatial description—What are the differences and why do they concern us? In: Naumenko, K., Aßmus, M. (eds.) Advanced Methods of Continuum Mechanics for Materials and Structures, pp. 3–28. Springer, Berlin (2016)CrossRef
39.
Ivanova, E.A., Vilchevskaya, E.N., Müller, W.H.: A study of objective time derivatives in material and spatial description. In: Altenbach, H., Goldstein, R., Murashkin, E. (eds.) Mechanics for Materials and Technologies. Advanced Structured Materials 46, pp. 195–229. Springer, Cham (2017)CrossRef
40.
Trangenstein, J.: Numerical Solution of Hyperbolic Partial Differential Ecuations, pp. 432–450. Cambridge University Press, Cambridge (2007)
41.
Versteeg, H.K., Malalasakera, W.: An introduction to Computational Fluid Mechanics, pp. 129–225. Pearson Education, New York (2007)
42.
Machado D.: Solucion numerica de las ecuaciones de Navier Stokes utilizando metodos tipo VOF, Universidad Simon Bolivar, Venezuela, pp. 30-45 (2019) (in spanish)
43.
Kamrin, K., Rycroft, C., Nave, J.C.: Reference map technique for finite-strain elasticity and fluid–solid interaction. J. Mech. Phys. 60, 1952–1969 (2012)ADSMathSciNetCrossRef
44.
Kamrin, K., Mani, A., Jain, S.: A conservative and non dissipative Eulerian formulation for the simulation of soft solids in fluids. J. Comput. Phys. 1, 261–289 (2019)MathSciNetMATH
45.
Tryggvasson, G., Prosperetti, A.: Computational Methods for multiphase flow, pp. 50–86. Cambridge University Press, Cambridge (2007)
46.
Tepole, A.: Growing skin: a computational model for skin expansion in reconstructive surgery. J. Mech. Phys. Solids 59, 2177–2190 (2011)ADSMathSciNetMATHCrossRef
47.
Metadaten
Titel
A new approach to solving the solid mechanics problems with matter supply
verfasst von
Elena A. Ivanova
Luis Eduardo Jatar Montaño
Publikationsdatum
04.05.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Continuum Mechanics and Thermodynamics / Ausgabe 4/2021
Print ISSN: 0935-1175
Elektronische ISSN: 1432-0959
DOI
https://doi.org/10.1007/s00161-021-01014-2

Weitere Artikel der Ausgabe 4/2021

Continuum Mechanics and Thermodynamics 4/2021 Zur Ausgabe

Original Article

Negative-stiffness composite systems and their coupled-field properties

Original Article

Elliptic functions and lattice sums for effective properties of heterogeneous materials

Original Article

Micropolar medium in a funnel-shaped crusher

Original Article

Lattice strain during compressive loading of AlCrFeNiTi multi-principal element alloys

Original Article

An extended Hamilton principle as unifying theory for coupled problems and dissipative microstructure evolution

Original Article

General approach to the modified Kirsch problem incorporating surface energy effects

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise