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
Erschienen in:
Mathematical Modeling of the Desiccation Cracking Kapitel lesen Erstes Kapitel lesen

2018 | OriginalPaper | Buchkapitel

Brief Introduction to Damage Mechanics and Its Relation to Deformations

verfasst von : Simon Grützner, Adrian Muntean

Erschienen in: Mathematical Analysis of Continuum Mechanics and Industrial Applications II

Verlag: Springer Singapore

Einloggen

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

search-config
loading …

Abstract

We discuss some principle concepts of damage mechanics and outline a possibility to address the open question of the damage-to-deformation relation by suggesting a parameter identification setting. To this end, we introduce a variable motivated by the physical damage phenomenon and comment on its accessibility through measurements. We give an extensive survey on analytic results and present an isotropic irreversible partial damage model in a dynamic mechanical setting in form of a second-order hyperbolic equation coupled with an ordinary differential equation for the damage evolution. We end with a note on a possible parameter identification setting.

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

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Integral Representation and Its Applications in Earthquake Mechanics: A Review
Nächstes Kapitel Structured Deformations of Continua: Theory and Applications
Fußnoten
1
Especially in the mechanics of solids, there are so-called anisotropic properties, whose response to external influences depends on the direction of those influences. Properties that do not show this directional dependency are referred to as isotropic.
 
2
This description separates damage mechanics from fracture or crack mechanics, respectively, which focuses on crack propagation rather than initiation.
 
3
Analytic results of the Kachanov-Rabotnov model are discussed in [1, 38], e.g.
 
4
Partial damage refers to a damage state \(0\le d\le \delta _0<1\), where \(\delta _0\) denotes the maximal damage possible. Partial damage models are more feasible for mathematical analysis, because they preserve uniform coercivity of the effective elasticity tensor, whereas complete damage leads to a degenerate momentum balance equation.
 
5
This approach was also continued in some subsequent publications of the author, e.g. in the analysis of a contact problem in an otherwise equal setting in [8] or a dynamic frictional contact problem of a visco-elastic material with damage in [7]. Both these articles further developed the ideas presented in [10].
 
6
For numeric investigations and results see [9].
 
7
This is why, as a long-term project, we aim to identify g. The only assumptions on g stem from the regularity needed to perform the analysis (see [18]).
 
Literatur
1.
Altenbach, H., Deuring, P., Naumenko, K.: A system of ordinary and partial differential equations describing creep behavior of thin-walled shells. Z. Ana. Anw. 18, 1003–1030 (1999)CrossRefMATH
2.
Bouchitté, G., Mielke, A., Roubíček, T.: A complete-damage problem at small strains. Z. Angew. Math. Phys 60, 205–236 (2009)MathSciNetCrossRefMATH
3.
Bonetti, E., Bonfanti, G.: Well-posedness results for a model of damage in thermoviscoelastic materials. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, 1187–1208 (2008)
4.
Bonetti, E., Schimperna, G., Segatti, A.: On a doubly nonlinear model for the evolution of damaging in viscoelastic materials. J. Differ. Equ. 218, 91–116 (2005)MathSciNetCrossRefMATH
5.
Bonetti, E., Schimperna, G.: Local existence for Frémond’s model of damage in elastic materials. Contin. Mech. Thermodyn. 16, 319–335 (2004)MathSciNetCrossRefMATH
6.
Bonetti, E., Frémond, M.: Damage theory: microscopic effects of vanishing macroscopic motions. Comput. Appl. Math. 22, 313–333 (2003)MathSciNetMATH
7.
Campo, M.A., Fernández, J.R., Kuttler, K.L.: Analysis of a dynamical frictional contact problem with damage. Fin. El. Anal. Des. 45, 659–674 (2009)CrossRef
8.
Campo, M.A., Fernández, J.R., Kuttler, K.L.: An elastic-viscoplastic quasistatic contact problem with damage. Comput. Methods Appl. Mech. Engrg 196, 3219–2339 (2007)MathSciNetCrossRefMATH
9.
Campo, M.A., Fernández, J.R., Kuttler, K.L., Shillor, M.: Quasistatic evolution of damage in an elastic body: numerical analysis and computational experiments. Appl. Numer. Math. 57, 976–988 (2007)MathSciNetCrossRefMATH
10.
Campo, M.A., Fernández, J.R., Han, W., Sofonea, M.: A dynamic viscoelastic contact problem with normal compliance and damage. Fin. Elem. Anal. Des. 42, 1–24 (2005)MathSciNetCrossRef
11.
Ciarlet, P.: Mathematical Elasticity, vol. I. North-Holland, Amsterdam (1988)MATH
12.
Farshbaf-Shaker, M.H., Heinemann, C.: A phase field approach for optimal boundary control of damage processes in two-dimensional viscoelastic media. Math. Models Methods Appl. Sci. 25, 2749–2793 (2015)MathSciNetCrossRefMATH
13.
Fiaschi, A., Knees, D., Stefanelli, U.: Young-measure quasi-static damage evolution. Arch. Rational Mech. Anal. 203, 415–453 (2012)MathSciNetCrossRefMATH
14.
Francfort, G.A., Garroni, A.: A variational view of partial brittle damage evolution. Arch. Ration. Mech. Anal. 182, 125–152 (2006)MathSciNetCrossRefMATH
15.
Frémond, M., Kuttler, K.L., Shillor, M.: Existence and uniqueness of solutions for a dynamic one-dimensional damage model. J. Math. Anal. Appl. 229, 271–294 (1999)MathSciNetCrossRefMATH
16.
Frémond, M., Nedjar, B.: Damage, gradient of damage and principle of virtual power. Int. J. Sol. Struct. 33, 1083–1103 (1996)MathSciNetCrossRefMATH
17.
Frémond, M., Nedjar, B.: Damage in concrete: the unilateral phenomenon. Nucl. Eng. Des. 156, 323–335 (1996)CrossRef
18.
Grützner, S.: An approach to parameter identification in damaged continua. Diploma thesis, University of Bremen (2015)
19.
Heinemann, C., Kraus, C.: Complete damage in linear elastic materials: modeling, weak formulation and existence results. Calc. Var. Partial Differ. Equ. 54, 217–250 (2015)MathSciNetCrossRefMATH
20.
Heinemann, C., Kraus, C.: Existence of weak solutions for a hyperbolic-parabolic phase field system with mixed boundary conditions on nonsmooth domains. SIAM J. Math. Anal. 47, 2044–2073 (2015)MathSciNetCrossRefMATH
21.
Heinemann, C., Kraus, C.: Existence of weak solutions for a pde system describing phase separation and damage processes including inertial effects. Discrete Contin. Dynam. Syst. 35, 2565–2590 (2015)MathSciNetCrossRefMATH
22.
Heinemann, C., Kraus, C.: Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes. Math. Bohem. 139, 315–331 (2014)MathSciNetMATH
23.
Heinemann, C., Kraus, C.: Existence results for diffuse interface models describing phase separation and damage. Eur. J. Appl. Math 24, 179–211 (2013)MathSciNetCrossRefMATH
24.
Heinemann, C., Kraus, C.: Existence of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21, 321–359 (2011)MathSciNetMATH
25.
Kogut, P.I., Leugering, G.: Optimal and approximate boundary controls of an elastic body with quasistatic evolution of damage. Math. Methods Appl. Sci. 38, 2739–2760 (2015)MathSciNetCrossRefMATH
26.
Kraus, C., Bonetti, E., Heinemann, C., Segatti, A.: Modeling and analysis of a phase field system for damage in phase separation processes in solids. J. Differ. Equ. 258, 3928–3959 (2015)MathSciNetCrossRefMATH
27.
Kuttler, K.L., Shillor, M.: Quasistatic evolution of damage in an elastic body. Nonlinear Anal. Real World Appl. 7, 674–699 (2006)
28.
Kuttler, K.L.: Quasistatic evolution of damage in an elastic-viscoplastic material. Elec. J. Differ. Equ. 2005, 1–25 (2005)MathSciNetMATH
29.
Lazzaroni, G., Rossi, R., Thomas, M., Toader, R.: Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics. J. Phys. Conf. Ser. 727 (2016)
30.
Lemaître, J., Chaboche, J.-.L: Mechanics of Solid Materials. Cambridge University Press, New York (1990)
31.
Lemaître, J., Dufailly, J.: Damage measurements. Eng. Fract. Mech. 28, 643–661 (1987)CrossRef
32.
Mainik, A., Mielke, A.: Existence results for energetic models for rate-independent systems. Calc. Var. Partial Differ. Equ. 22, 73–99 (2005)MathSciNetCrossRefMATH
33.
Mielke, A., Roubíček, T.: Rate-independent damage processes in nonlinear elasticity. Math. Mod. Methods Appl. Sci. 16, 177–209 (2006)MathSciNetCrossRefMATH
34.
Mielke, A.: Evolution of rate-independent systems. In: Dafermos, C.M., Feireisl, E. (eds.) Handbook of Differential Equations. 461–559. Elsevier, Amsterdam (2005)
35.
Murakami, S.: Continuum Damage Mechanics. Springer, Heidelberg (2012)CrossRef
36.
Nedjar, B.: Damage and gradient of damage in transient dynamics. In: IUTAM Argoul, P., Frémond, M., Nguyen, Q.S. (eds.) IUTAM Symposium on Variations of Domain and Free-Boundary Problems in Solid Mechanics. Proceedings of the IUTAM Symosium held in Paris, France, April 22-25, 1997; 189–196. Springer, Berlin (1999)
37.
Roubíček, T., Tomassetti, G.: Thermomechanics of damageable materials under diffusion: modelling and analysis. Z. Angew. Math. Phys. 66, 3535–3572 (2016)MathSciNetCrossRefMATH
38.
39.
40.
Thomas, M., Mielke, A.: Damage of nonlinearly elastic materials at small strain - existence and regularity results. Z. Angew. Math. Mech. 90, 88–112 (2010)MathSciNetCrossRefMATH
41.
Voyiadjis, G.Z., Kattan, P.I.: Advances in Damage Mechanics. Elsevier, Amsterdam (2006)MATH
Metadaten
Titel
Brief Introduction to Damage Mechanics and Its Relation to Deformations
verfasst von
Simon Grützner
Adrian Muntean
Copyright-Jahr
2018
Verlag
Springer Singapore
Buch
Mathematical Analysis of Continuum Mechanics and Industrial Applications II

Print ISBN: 978-981-10-6282-7

Electronic ISBN: 978-981-10-6283-4

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-981-10-6283-4_10

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