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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Abbreviations
- A :
-
Cross-sectional area
- \( \overline{A} \) :
-
Effective cross-sectional area
- ϕ :
-
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)
C. Basaran, C.Y. Yan, A thermodynamic framework for damage mechanics of solder joints. Trans. ASME J. Electron. Packag. 120, 379–384 (1998)
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)
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)
I. Doghri, Mechanics of Deformable Solids: Linear and Nonlinear, Analytical and Computational Aspects (Springer, 2000)
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)
L. Kachanov, On the creep fracture time. Izv. Akad. Nauk USSR Otd. Tech. 8, 26–31 (1958) (in Russian)
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)
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)
P.I. Kattan, G.Z. Voyiadjis, Decomposition of damage tensor in continuum damage mechanics. J. Eng. Mech. ASCE 127(9), 940–944 (2001a)
P.I. Kattan, G.Z. Voyiadjis, Damage Mechanics with Finite Elements: Practical Applications with Computer Tools (Springer, 2001b)
D. Krajcinovic, Damage Mechanics (North Holland, 1996), 776 page
P. Ladeveze, J. Lemaitre, Damage effective stress in quasi-unilateral conditions, in The 16th International Congress of Theoretical and Applied Mechanics, Lyngby (1984)
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
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)
G. Lubineau, A pyramidal modeling scheme for laminates – identification of transverse cracking. Int. J. Damage Mech. 19(4), 499–518 (2010)
G. Lubineau, P. Ladeveze, Construction of a micromechanics-based intralaminar mesomodel, and illustrations in ABAQUS/standard. Comput. Mater. Sci. 43(1), 137–145 (2008)
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
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)
F. Sidoroff, Description of anisotropic damage application in elasticity, in IUTAM Colloqium on Physical Nonlinearities in Structural Analysis (Springer, Berlin, 1981), pp. 237–244
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)
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)
G.Z. Voyiadjis, P.I. Kattan, Damage Mechanics (Taylor and Francis (CRC Press), 2005)
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)
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)
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)
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
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
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
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)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this entry
Cite this entry
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-60242-0_85
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-60241-3
Online ISBN: 978-3-030-60242-0
eBook Packages: EngineeringReference Module Computer Science and Engineering