Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Some Revisions of Fatigue Crack Growth Characteristics of Rubber Read chapter Read first chapter

2021 | OriginalPaper | Chapter

New Approaches to Modeling Failure and Fracture of Rubberlike Materials

Author : K. Y. Volokh

Published in: Fatigue Crack Growth in Rubber Materials

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this chapter we review some recent approaches to modeling failure and fracture of soft materials. By failure we mean the onset of damage via material instability. By fracture we mean further localization of damage into cracks with their subsequent propagation.
Mathematical description of failure is simple and it only requires some bounding of the strain energy density. The bounded strain energy automatically implies the bounded achievable stress, which is an indicator of material failure. By bounding the strain energy via energy limiters we show, for instance, how to explain cavitation, analyze strength of soft composites, and predict direction of possible cracks.
Mathematical description of fracture is more involved because it requires regularized formulations suppressing the so-called pathological mesh sensitivity. Most existing approaches utilize purely formal regularization schemes that lack physical grounds. We discuss a more physically based approach rooted in the idea that bulk cracks are not a peaceful unzipping of adjacent atomic layers but rather a catastrophic explosion of bonds localized within a finite characteristic area.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now
previous chapter Cavitation Micro-mechanisms in Silica-Filled Styrene-Butadiene Rubber Upon Fatigue and Cyclic Tensile Testing
next chapter Influence of Filler Induced Cracks on the Statistical Lifetime of Rubber: A Review
Footnotes
1
These works were not devoted to soft materials per se.
 
2
For example, the authors of [63] rightfully note that “although the length-scale parameter associated with the phase-field approximation is introduced as a numerical parameter it is, in fact, a material parameter that influences the critical stress at which crack nucleation occurs.”
 
Literature
1.
Volokh KY (2019) Mechanics of soft materials. Springer, Singapore
2.
Truesdell C, Noll W (2004) The non-linear field theories of mechanics. Springer, Berlin
3.
Simo JC (1987) On a fully three-dimensional finite strain viscoelastic damage model: formulation and computational aspects. Comp Meth Appl Mech Eng 60:153–173
4.
Govindjee S, Simo JC (1991) A micro-mechanically based continuum damage model of carbon black-filled rubbers incorporating the mullins effect. J Mech Phys Solids 39:87–112
5.
Johnson MA, Beatty MF (1993) A constitutive equation for the Mullins effect in stress controlled in uniaxial extension experiments. Cont Mech Therm 5:301–318
6.
Miehe C (1995) Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials. Eur J Mech A/Solids 14:697–720
7.
De Souza Neto EA, Peric D, Owen DRJ (1998) Continuum modeling and numerical simulation of material damage at finite strains. Arch Comp Meth Eng 5:311–384
8.
Ogden RW, Roxburgh DG (1999) A pseudo-elastic model for the Mullins effect in filled rubber. Proc Roy Soc Lond Ser A 455:2861–2877
9.
Menzel A, Steinmann P (2001) A theoretical and computational framework for anisotropic continuum damage mechanics at large strains. Int J Solids Struct 38:9505–9523
10.
Guo Z, Sluys L (2006) Computational modeling of the stress-softening phenomenon of rubber like materials under cyclic loading. Eur J Mech A/Solids 25:877–896
11.
De Tommasi D, Puglisi G, Saccomandi G (2008) Localized vs diffuse damage in amorphous materials. Phys Rev Lett 100:085502.PubMed
12.
Dal H, Kaliske M (2009) A micro-continuum-mechanical material model for failure of rubberlike materials: application to ageing-induced fracturing. J Mech Phys Solids 57:1340–1356
13.
Volokh KY (2013) Review of the energy limiters approach to modeling failure of rubber. Rubber Chem Technol 86:470–487
14.
Volokh KY (2007) Hyperelasticity with softening for modeling materials failure. J Mech Phys Solids 55:2237–2264
15.
Volokh KY (2010) On modeling failure of rubberlike materials. Mech Res Commun 37:684–689
16.
Volokh KY (2014) On irreversibility and dissipation in hyperelasticity with softening. J Appl Mech 81:074501
17.
Hamdi A, Nait Abdelaziz M, Ait Hocine N, Heuillet P, Benseddiq N (2006) A fracture criterion of rubber-like materials under plane stress conditions. Polym Test 25:994–1005
18.
Gent AN, Lindley PB (1959) Internal rupture of bonded rubber cylinders in tension. Proc Roy Soc A 2:195–205
19.
Ball JM (1982) Discontinuous equilibrium solutions and cavitation in nonlinear elasticity. Phil Trans Roy Soc Lond A 306:557–610
20.
Lev Y, Volokh KY (2016) On cavitation in rubberlike materials. J Appl Mech 83:044501
21.
Volokh KY (2011) Cavitation instability in rubber. Int J Appl Mech 3:29311
22.
Volokh KY (2015) Cavitation instability as a trigger of aneurysm rupture. Biomech Model Mechanobiol 14:1071–1079PubMed
23.
Faye A, Rodrguez-Martnez JA, Volokh KY (2017) Spherical void expansion in rubber-like materials: the stabilizing effects of viscosity and inertia. Int J Non-Linear Mech 92:118–126
24.
Lev Y, Faye A, Volokh KY (2019) Thermoelastic deformation and failure of rubberlike materials. J Mech Phys Solids 122:538–554
25.
Aboudi J, Volokh KY (2015) Failure prediction of unidirectional composites undergoing large deformations. J Appl Mech 82:071004
26.
Volokh KY, Aboudi J (2016) Aneurysm strength can decrease under calcification. J Mech Behav Biomed Mater 57:164–174PubMed
27.
Slesarenko V, Volokh KY, Aboudi J, Rudykh S (2017) Understanding the strength of bioinspired soft composites. Int J Mech Sci 131–132:171–178
28.
Volokh KY (2017) Loss of ellipticity in elasticity with energy limiters. Eur J Mech A Solids 63:36–42
29.
Mythravaruni P, Volokh KY (2018) Failure of rubber bearings under combined shear and compression. J Appl Mech 85:074503
30.
Mythravaruni P, Volokh KY (2019) On incompressibility constraint and crack direction in soft solids. J Appl Mech 86:101004
31.
Volokh KY (2019) Constitutive model of human artery adventitia enhanced with a failure description. Mech Soft Mater 1:8
32.
Mythravaruni P, Volokh KY (2020) On the onset of cracks in arteries. Mol Cell Biomech 17:1–17
33.
Takahashi Y (2012) Damage of rubber bearings and dumpers of bridges in 2011 great East Japan earthquake. Proceedings of the International Symposium on Engineering, Lessons Learned from the 2011 Great East Japan Earthquake, March 1–4, Tokyo, Japan
34.
Lee S, Pharr M (2019) Sideways and stable crack propagation in a silicone elastomer. PNAS 116:9251–9256PubMed
35.
Sugita S, Matsumoto T (2017) Local distribution of collagen fibers determines crack initiation site and its propagation direction during aortic rupture. Biomech Model Mechnobiol 17:577–587
36.
Griffith AA (1921) The phenomena of rupture and flow in solids. Philos Trans R Soc Lond A 221:163–198
37.
Volokh KY, Trapper P (2008) Fracture toughness from the standpoint of softening hyperelasticity. J Mech Phys Solids 56:2459–2472
38.
Barenblatt GI (1959) The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks. J Appl Math Mech 23:622–636
39.
Needleman A (1987) A continuum model for void nucleation by inclusion debonding. J Appl Mech 54:525–531
40.
Rice JR, Wang JS (1989) Embrittlement of interfaces by solute segregation. Mater Sci Eng A 107:23–40
41.
Tvergaard V, Hutchinson JW (1992) The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J Mech Phys Solids 40:1377–1397
42.
Camacho GT, Ortiz M (1996) Computational modeling of impact damage in brittle materials. Int J Solids Struct 33:2899–2938
43.
de Borst R (2001) Some recent issues in computational failure mechanics. Int J Numer Meth Eng 52:63–95
44.
Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42:1397–1434
45.
Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack without remeshing. Int J Num Meth Eng 46:131–150
46.
Park K, Paulino GH, Roesler JR (2009) A unified potential-based cohesive model of mixed-mode fracture. J Mech Phys Solids 57:891–908
47.
Gong B, Paggi M, Carpinteri A (2012) A cohesive crack model coupled with damage for interface fatigue problems. Int J Fract 137:91–104
48.
Kachanov LM (1958) Time of the rupture process under creep conditions. Izvestiia Akademii Nauk SSSR, Otdelenie Teckhnicheskikh Nauk 8:26–31
49.
Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part I-yield criteria and flow rules for porous ductile media. J Eng Mat Tech 99:2–151
50.
Voyiadjis GZ, Kattan PI (1992) A plasticity-damage theory for large deformation of solids—I. Theoretical formulation. Int J Eng Sci 30:1089–1108
51.
Gao H, Klein P (1998) Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds. J Mech Phys Solids 46:187–218
52.
Klein P, Gao H (1998) Crack nucleation and growth as strain localization in a virtual-bond continuum. Eng Fract Mech 61:21–48
53.
Lemaitre J, Desmorat R (2005) Engineering damage mechanics: ductile, creep, fatigue and brittle failures. Springer, Berlin
54.
Volokh KY (2004) Nonlinear elasticity for modeling fracture of isotropic brittle solids. J Appl Mech 71:141–143
55.
Benzerga AA, Leblond JB, Needleman A, Tvergaard V (2016) Ductile failure modeling. Int J Fract 201:29–80
56.
Pijaudier-Cabot G, Bazant ZP (1987) Nonlocal damage theory. J Eng Mech 113:1512–1533
57.
Lasry D, Belytschko T (1988) Localization limiters in transient problems. Int J Solids Struct 24:581–597
58.
Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree JHP (1996) Gradient enhanced damage for quasi-brittle materials. Int J Num Meth Eng 39:3391–3403
59.
de Borst R, van der Giessen E (1998) Material instabilities in solids. Wiley, Chichester
60.
Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209
61.
Francfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46:1319–1342
62.
Hofacker M, Miehe C (2012) Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation. Int J Fract 178:113–129
63.
Borden MJ, Verhoosel CV, Scott MA, Hughes TJR, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comp Meth Appl Mech Eng 217–220:77–95
64.
Volokh KY (2017) Fracture as a material sink. Mater Theory 1:3
65.
Persson BNJ, Albohr O, Heinrich G, Ueba H (2005) Crack propagation in rubber-like materials. J Phys Condens Matter 17:R1071–R1142
66.
Faye A, Lev Y, Volokh KY (2019) The effect of local inertia around the crack tip in dynamic fracture of soft materials. Mech Soft Mater 1:4
67.
Chen CH, Bouchbinder E, Karma A (2017) Instability in dynamic fracture and the failure of the classical theory of cracks. Nat Phys 13:1186
68.
Agrawal V, Dayal K (2017) Dependence of equilibrium Griffith surface energy on crack speed in phase-field models for fracture coupled to elastodynamics. Int J Fract 207:243–249
Metadata
Title
New Approaches to Modeling Failure and Fracture of Rubberlike Materials
Author
K. Y. Volokh
Copyright Year
2021
Book
Fatigue Crack Growth in Rubber Materials

Print ISBN: 978-3-030-68919-3

Electronic ISBN: 978-3-030-68920-9

Copyright Year: 2021

DOI
https://doi.org/10.1007/12_2020_64

Premium Partners

    Image Credits