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Partial Damage Mechanics: Introduction

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Handbook of Damage Mechanics

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Abstract

In this work, advanced models for material damage in metals are presented. The models are based on new concepts in continuum damage mechanics, namely, the concept of partial damage modeling. This new concept is illustrated both mathematically and graphically. The classical equations of damage mechanics are obtained as special cases of the equations of partial damage mechanics. It is hoped that this work lays the groundwork for new avenues of research in damage mechanics and materials science.

In this work advanced models for material damage in metals are presented. The models are based on new concepts in continuum damage mechanics, namely, the concept of partial damage modeling. This new concept is illustrated both mathematically and graphically. The classical equations of damage mechanics are obtained as special cases of the equations of partial damage mechanics. It is hoped that this work lays the groundwork for new avenues of research in damage mechanics and materials science.

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Abbreviations

A :

Cross-sectional area

\( \overline{A} \) :

Effective cross-sectional area

Ï• :

Total damage variable

σ :

Cauchy stress

\( \overline{\sigma} \) :

Effective Cauchy stress

ε :

Strain

\( \overline{\varepsilon} \) :

Effective strain

n :

Exponent

\( \tilde{\phi} \) :

Partial damage variable

α :

Partial damage fraction

ϕ ∗ :

Damage variable associated with partial damage

\( \tilde{\sigma} \) :

Effective Cauchy stress associated with partial damage

e :

Exponential function

{σ}:

Stress vector

\( \left\{\overline{\sigma}\right\} \) :

Effective stress vector

[M]:

Fourth-rank damage effect tensor

\( \left[\tilde{M}\right] \) :

Fourth-rank partial damage effect tensor

[M∗]:

Fourth-rank damage effect tensor associated with partial damage

[I4]:

Fourth-rank identity tensor

References

  • C. Basaran, S. Nie, An irreversible thermodynamic theory for damage mechanics of solids. Int. J. Damage Mech. 13(3), 205–224 (2004)

    Article  Google Scholar 

  • C. Basaran, C.Y. Yan, A thermodynamic framework for damage mechanics of solder joints. Trans. ASME J. Electron. Packag. 120, 379–384 (1998)

    Article  Google Scholar 

  • D.J. Celentano, P.E. Tapia, J.-L. Chaboche, Experimental and numerical characterization of damage evolution in steels, in Mecanica Computacional, vol. XXIII, ed. by G. Buscaglia, E. Dari, O. Zamonsky (Bariloche, 2004)

    Google Scholar 

  • M.K. Darabi, R.K. Abu Al-Rub, D.N. Little, A continuum damage mechanics framework for modeling micro-damage healing. Int. J. Solids Struct. 49, 492–513 (2012)

    Article  Google Scholar 

  • I. Doghri, Mechanics of Deformable Solids: Linear and Nonlinear, Analytical and Computational Aspects (Springer, 2000)

    Book  Google Scholar 

  • N.R. Hansen, H.L. Schreyer, A thermodynamically consistent framework for theories of elastoplasticity coupled with damage. Int. J. Solids Struct 31(3), 359–389 (1994)

    Article  Google Scholar 

  • L. Kachanov, On the creep fracture time. Izv. Akad. Nauk USSR Otd. Tech. 8, 26–31 (1958) (in Russian)

    Google Scholar 

  • P.I. Kattan, G.Z. Voyiadjis, A coupled theory of damage mechanics and finite strain elasto-plasticity – part I: damage and elastic deformations. Int. J. Eng. Sci. 28(5), 421–435 (1990)

    Article  Google Scholar 

  • P.I. Kattan, G.Z. Voyiadjis, A plasticity-damage theory for large deformation of solids – part II: applications to finite simple shear. Int. J. Eng. Sci. 31(1), 183–199 (1993)

    Article  Google Scholar 

  • P.I. Kattan, G.Z. Voyiadjis, Decomposition of damage tensor in continuum damage mechanics. J. Eng. Mech. ASCE 127(9), 940–944 (2001a)

    Article  Google Scholar 

  • P.I. Kattan, G.Z. Voyiadjis, Damage Mechanics with Finite Elements: Practical Applications with Computer Tools (Springer, 2001b)

    Google Scholar 

  • D. Krajcinovic, Damage Mechanics (North Holland, 1996), 776 page

    Google Scholar 

  • P. Ladeveze, J. Lemaitre, Damage effective stress in quasi-unilateral conditions, in The 16th International Congress of Theoretical and Applied Mechanics, Lyngby (1984)

    Google Scholar 

  • P. Ladeveze, M. Poss, L. Proslier, Damage and fracture of tridirectional composites, in Progress in Science and Engineering of Composites. Proceedings of the Fourth International Conference on Composite Materials, vol. 1 (Japan Society for Composite Materials, 1982), pp. 649–658

    Google Scholar 

  • H. Lee, K. Peng, J. Wang, An anisotropic damage criterion for deformation instability and its application to forming limit analysis of metal plates. Eng. Fract. Mech. 21, 1031–1054 (1985)

    Article  Google Scholar 

  • G. Lubineau, A pyramidal modeling scheme for laminates – identification of transverse cracking. Int. J. Damage Mech. 19(4), 499–518 (2010)

    Article  MathSciNet  Google Scholar 

  • G. Lubineau, P. Ladeveze, Construction of a micromechanics-based intralaminar mesomodel, and illustrations in ABAQUS/standard. Comput. Mater. Sci. 43(1), 137–145 (2008)

    Article  Google Scholar 

  • Y. Rabotnov, Creep rupture, in Proceedings, Twelfth International Congress of Applied Mechanics, Stanford, 1968, ed. by M. Hetenyi, W. G. Vincenti (Springer, Berlin, 1969), pp. 342–349

    Google Scholar 

  • J.R. Rice, Inelastic constitutive relations for solids: an internal variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19, 433–455 (1971)

    Article  Google Scholar 

  • F. Sidoroff, Description of anisotropic damage application in elasticity, in IUTAM Colloqium on Physical Nonlinearities in Structural Analysis (Springer, Berlin, 1981), pp. 237–244

    Google Scholar 

  • G.Z. Voyiadjis, P.I. Kattan, A coupled theory of damage mechanics and finite strain elasto-plasticity – part II: damage and finite strain plasticity. Int. J. Eng. Sci. 28(6), 505–524 (1990)

    Article  Google Scholar 

  • G.Z. Voyiadjis, P.I. Kattan, A plasticity-damage theory for large deformation of solids – part I: theoretical formulation. Int. J. Eng. Sci. 30(9), 1089–1108 (1992)

    Article  Google Scholar 

  • G.Z. Voyiadjis, P.I. Kattan, Damage Mechanics (Taylor and Francis (CRC Press), 2005)

    Book  Google Scholar 

  • G.Z. Voyiadjis, P.I. Kattan, Advances in Damage Mechanics: Metals and Metal Matrix Composites with an Introduction to Fabric Tensors, 2nd edn. (Elsevier, 2006)

    Google Scholar 

  • G.Z. Voyiadjis, P.I. Kattan, A comparative study of damage variables in continuum damage mechanics. Int. J. Damage Mech. 18(4), 315–340 (2009)

    Article  Google Scholar 

  • G.Z. Voyiadjis, P.I. Kattan, Mechanics of damage processes in series and in parallel: a conceptual framework. Acta Mech. 223(9), 1863–1878 (2012)

    Article  Google Scholar 

  • G.Z. Voyiadjis, P.I. Kattan, Mechanics of damage, healing, damageability, and integrity of materials: a conceptual framework. Int. J. Damage Mech. 26(1), 50–103 (2017a). https://doi.org/10.1177/1056789516635730

    Article  Google Scholar 

  • G.Z. Voyiadjis, P.I. Kattan, Decomposition of elastic stiffness degradation in continuum damage mechanics. J. Eng. Mater. Technol. ASME 139(2), 021005-1–021005-15 (2017b). https://doi.org/10.1115/1.4035292

    Article  Google Scholar 

  • G.Z. Voyiadjis, P.I. Kattan, Introducing damage mechanics templates for the consistent and systematic formulation of holistic material damage models. Acta Mech. 228(3), 951–990 (2017c). https://doi.org/10.1007/s00707-016-1747-6

    Article  MathSciNet  MATH  Google Scholar 

  • G.Z. Voyiadjis, A. Shojaei, G. Li, A thermodynamic consistent damage and healing model for self-healing materials. Int. J. Plast. 27(7), 1025–1044 (2011)

    Article  Google Scholar 

  • G.Z. Voyiadjis, A. Shojaei, G. Li, P.I. Kattan, A theory of anisotropic healing and damage mechanics of materials. Proc. R. Soc. A Math. Phys. Eng. Sci. 468(2137), 163–183 (2012a)

    MathSciNet  MATH  Google Scholar 

  • G.Z. Voyiadjis, A. Shojaei, G. Li, P.I. Kattan, Continuum damage-healing mechanics with introduction to new healing variables. Int. J. Damage Mech. 21, 391–414 (2012b)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Center for GeoInformatics C4G and Computational Solid Mechanics Laboratory, Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA, USA

    George Z. Voyiadjis

  2. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA, USA

    Peter I. Kattan

Authors
  1. George Z. Voyiadjis
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  2. Peter I. Kattan
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Corresponding author

Correspondence to Peter I. Kattan .

Editor information

Editors and Affiliations

  1. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA, USA

    George Z. Voyiadjis

Section Editor information

  1. Independent Researcher, Petra Books, Amman, Jordan

    Peter I. Kattan

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Voyiadjis, G.Z., Kattan, P.I. (2022). Partial Damage Mechanics: Introduction. In: Voyiadjis, G.Z. (eds) Handbook of Damage Mechanics . Springer, Cham. https://doi.org/10.1007/978-3-030-60242-0_85

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