In this work, the principles of damage/healing mechanics are first reviewed. This is followed by introducing the concept of super healing of materials in the framework of continuum damage mechanics. Once a damaged material is healed and the damage is recovered, further healing results in a strengthened material. This process of added healing beyond what is necessary to recover damage is termed here super healing. In super healing, the material gains stiffness and the end and final objective of the super healing process is to reach what is called the Super Material. The second part of this work generalizes these concepts to anisotropic damage and healing of materials. The concept of anisotropic super healing is also introduced. An example is presented for the case of plane stress where the mechanics of damage/healing and super healing are demonstrated. Finally, the characteristics of the elusive Super Material are postulated.
AdamJA (1999) A simplified model of wound healing (with particular reference to the critical size defect). Mathematical and Computer Modeling30: 23–32.
2.
BarberoEJGrecoFLonettiP (2005) Continuum damage-healing mechanics with application to self-healing composites. International Journal of Damage Mechanics14: 51–81.
3.
CauvinATestaRB (1999) Damage mechanics: basic variables in continuum theories. International Journal of Solids and Structures36: 747–761.
4.
ChabocheJL (1991) On some modifications of kinematic hardening to improve the description of ratcheting effects. International Journal of Plasticity7: 661–678.
5.
ChabocheJL (1997) Thermodynamic formulation of constitutive equations and applications to the viscoplasticity and viscoelasticity of metals and polymers. International Journal of Solids and Structures34: 2239–2254.
6.
ChowCLJieM (2009) Anisotropic damage-coupled sheet metal forming limit analysis. International Journal of Damage Mechanics18: 371–392.
7.
DarabiMAbu Al-RubRLittleDN (2012) A continuum damage mechanics framework for modeling micro-damage healing. International Journal of Solids and Structures49: 492–513.
8.
HansenNRSchreyerHL (1994) A thermodynamically consistent framework for theories of elastoplasticity coupled with damage. International Journal of Solids and Structures31(3): 359–389.
9.
JohnMLiG (2010) Self-healing of sandwich structures with grid stiffened shape memory polymer syntactic foam core. Smart Materials and Structures19: 1–12.
10.
JuJWChenTM (1994a) Effective elastic moduli of two-dimensional brittle solids with interacting microcracks – part I: basic formulations. ASME, Journal of Applied Mechanics61: 349–357.
11.
JuJWChenTM (1994b) Effective elastic moduli of two-dimensional brittle solids with interacting microcracks – part I: evolutionary damage models. ASME, Journal of Applied Mechanics61: 358–366.
12.
JuJWYuanKY (2012) New strain energy based coupled elastoplastic two-parameter damage and healing models for earth moving processes. International Journal of Damage Mechanics21(7): 989–1019.
13.
JuJWYuanKYKuoAW (2012a) Novel strain energy based coupled elastoplastic damage and healing models for geomaterials – part I: formulations. International Journal of Damage Mechanics21(4): 525–549.
14.
JuJWYuanKYKuoAW (2012b) Novel strain energy based coupled elastoplastic damage and healing models for geomaterials – part II: computational aspects. International Journal of Damage Mechanics21(4): 551–576.
15.
KachanovL (1958) On the creep fracture time. Izv Akad, Nauk USSR Otd Tech8: 26–31; [in Russian].
16.
KattanPIVoyiadjisGZ (1990) A coupled theory of damage mechanics and finite strain elasto-plasticity – part I: damage and elastic deformations. International Journal of Engineering Science28(5): 421–435.
17.
KattanPIVoyiadjisGZ (1993) A plasticity-damage theory for large deformation of solids – part II: applications to finite simple shear. International Journal of Engineering Science31(1): 183–199.
18.
KattanPIVoyiadjisGZ (2001a) Decomposition of damage tensor in continuum damage mechanics. Journal of Engineering Mechanics, ASCE127(9): 940–944.
19.
KattanPIVoyiadjisGZ (2001b) Damage Mechanics with Finite Elements: Practical Applications with Computer Tools, Germany: Springer-Verlag.
20.
Ladeveze P and Lemaitre J (1984) Damage effective stress in quasi-unilateral conditions. In: The 16th international congress of theoretical and applied mechanics, Lyngby, Denmark.
21.
Ladeveze P, Poss M and Proslier L (1982) Damage and fracture of tridirectional composites, in progress in science and engineering of composites. In: Proceedings of the fourth international conference on composite materials, Japan Society for Composite Materials, [Vol. 1], pp.649–658.
22.
LeeHPengKWangJ (1985) An anisotropic damage criterion for deformation instability and its application to forming limit analysis of metal plates. Engineering Fracture Mechanics21: 1031–1054.
23.
LemaitreJ (1984) How to use damage mechanics. Nuclear Engineering and Design80: 233–245.
24.
LemaitreJ (1985) Coupled elastoplasticity and damage constitutive equations. Computer Methods in Applied Mechanics and Engineering51: 31–49.
25.
LemaitreJChabocheJL (1990) Mechanics of Solid Materials, Cambridge: Cambridge University Press.
26.
LiGJohnM (2008) A self-healing smart syntactic foam under multiple impacts. Composites Science and Technology68: 3337–3343.
27.
LiGNettlesD (2010) Thermomechanical characterization of a shape memory polymer self-repairing syntactic foam. Polymer51: 755–762.
28.
LiGUppuN (2010) Shape memory polymer based self-healing syntactic foam: 3-D confined thermomechanical characterization. Composite Science and Technology70: 1419–1427.
29.
LiuYLChenYW (2007) Thermally reversible cross-linked polyamides with high toughness and self-repairing ability from maleimide- and furan-functionalized aromatic polyamides. Macromolecular Chemistry and Physics208: 224–232.
30.
LubardaVAKrajcinovicD (1993) Damage tensors and the crack density distribution. International Journal of Solids and Structures30: 2859–2877.
31.
MiaoSWangMLSchreyerHL (1995) Constitutive models for healing of materials with application to compaction of crushed rock salt. ASCE, Journal of Engineering Mechanics121: 1122–11129.
32.
NjiJLiG (2010a) A self-healing 3D woven fabric reinforced shape memory polymer composite for impact mitigation. Smart Materials and Structures19: 1–9.
33.
NjiJLiG (2010b) A biomimic shape memory polymer based self-healing particulate composite. Polymer51: 6021–6029.
34.
PangJWCBondIP (2005) A hollow fiber reinforced polymer composite encompassing self-healing and enhanced damage visibility. Composites Science and Technology65: 1791–1799.
35.
QiuJvan de VenMWuS (2012) Evaluating self-healing capability of bituminous materials. Experimental Mechanics52: 1163–1171.
36.
Rabotnov Y (1969) Creep rupture. In: Proceedings, twelfth international congress of applied mechanics, (eds M Hetenyi and WG Vincenti), Stanford, 26–31 August 1968, pp.342–349. Berlin: Springer-Verlag.
37.
Sidoroff F (1981) Description of anisotropic damage application in elasticity. In: IUTAM colloquium on physical nonlinearities in structural analysis, pp.237–244. Berlin: Springer-Verlag.
38.
SimpsonAHRWGardnerTNEvansM (2000) Stiffness, strength, and healing assessment in different bone fractures – a simple mathematical model. Injury31: 777–781.
39.
TooheyKSSottosNRLewisJA (2007) Self-healing materials with microvascular networks. Nature Materials6: 581–585.
40.
VarleyRJvan der ZwaagS (2008) Towards an understanding of thermally activated self-healing of an ionomer system during ballistic penetration. Acta Materialia56: 5737–5750.
41.
VoyiadjisGZ (1988) Degradation of elastic modulus in elastoplastic coupling with finite strains. International Journal of Plasticity4: 335–353.
42.
VoyiadjisGZKattanPI (1990) A coupled theory of damage mechanics and finite strain elasto-plasticity – part II: damage and finite strain plasticity. International Journal of Engineering Science28(6): 505–524.
43.
VoyiadjisGZKattanPI (1992) A plasticity-damage theory for large deformation of solids – part I: theoretical formulation. International Journal of Engineering Science30(9): 1089–1108.
44.
VoyiadjisGZKattanPI (2005) Damage Mechanics, Florida, USA: Taylor and Francis (CRC Press).
45.
VoyiadjisGZKattanPI (2006a) Advances in Damage Mechanics: Metals and Metal Matrix Composites with an Introduction to Fabric Tensors, 2nd ed. The Netherlands: Elsevier.
46.
VoyiadjisGZKattanPI (2006b) A new fabric-based damage tensor. Journal of the Mechanical Behavior of Materials17(1): 31–56.
47.
VoyiadjisGZKattanPI (2006c) Damage mechanics with fabric tensors. Mechanics of Advanced Materials and Structures13(4): 285–301.
48.
VoyiadjisGZKattanPI (2009) A comparative study of damage variables in continuum damage mechanics. International Journal of Damage Mechanics18(4): 315–340.
49.
VoyiadjisGZKattanPI (2012a) A new class of damage variables in continuum damage mechanics. ASME Journal of Engineering Materials and Technology134(2): 021016, 1–10.
50.
Voyiadjis GZ and Kattan PI (2012b) Introduction to the mechanics and design of undamageable materials. International Journal of Damage Mechanics. Epub ahead of print 26 April 2012. DOI: 10.1177/1056789512446518; [13 manuscript pages].
51.
VoyiadjisGZKattanPI (2012c) Mechanics of damage processes in series and in parallel: a conceptual framework. Acta Mechanica223(9): 863–1878.
52.
Voyiadjis GZ and Kattan PI (2013) On the theory of elastic undamageable materials. ASME Journal of Engineering Materials and Technology [accepted for publication].
53.
VoyiadjisGZShojaeiALiG (2011) A thermodynamic consistent damage and healing model for self-healing materials. International Journal of Plasticity27: 1025–1044.
54.
VoyiadjisGZShojaeiALiG (2012a) Continuum damage-healing mechanics with introduction to new healing variables. International Journal of Damage Mechanics21(3): 391–414.
55.
VoyiadjisGZShojaeiALiG (2012b) A theory of anisotropic healing and damage mechanics of materials. Proc R Soc A468: 163–183.
56.
VoyiadjisGZYousefMAKattanPI (2012c) New tensors for anisotropic damage in continuum damage mechanics. ASME Journal of Engineering Materials and Technology134(2): 021015, 1–10.
57.
WhiteSRSottosNRGeubellePH (2001) Autonomic healing of polymer composites. Nature409: 794–797.
58.
YuanKYJuJW (2012) New strain-energy based coupled elastoplastic damage-healing formulations accounting for effect of matrix suction during earth moving processes. ASCE, Journal of Engineering Mechanics21(4): 525–549. [39 pages, accepted for publication].
59.
ZakoMTakanoN (1999) Intelligent materials systems using epoxy particles to repair microcracks and delamination damage in GFRP. Journal of Intelligent Material Systems and Structures10: 836–841.
