Macroscopical modeling and numerical simulation for the characterization of crack and durability properties of particle-reinforced elastomers

Lecture Notes in Applied and Computational Mechanics

Volumn 70, Issue , 2013, Pages 167-226

  Behnke, Ronny ^a   Dal, Hüsnü ^b   Geißler, Gordon ^c   Näser, Bastian ^d   Netzker, Christiane ^e   Kaliske, Michael ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF STUTTGART   (Germany)

^c DYNAMORE GMBH   (Germany)

^d DASSAULT SYSTÈMES   (France)

^e DAIMLER AG   (Germany)

Author keywords

Durability; Elastomeric material; Endochronic plasticity; Fracture; Macroscopical modeling; Material forces; Numerical simulation; Visco elasticity

Indexed keywords

ADAPTIVE IMPLEMENTATION; DISSIPATIVE PROPERTIES; ELASTOMERIC MATERIALS; EXPERIMENTAL OBSERVATION; FINITE VISCOELASTICITIES; MATERIAL FORCE METHOD; MATERIAL FORCES; MECHANICAL PARAMETERS;

COMPUTER SIMULATION; CRACK PROPAGATION; DURABILITY; ELASTICITY; ELASTOMERS; FRACTURE; NUMERICAL MODELS; REINFORCED PLASTICS; REINFORCEMENT; RUBBER; STATISTICAL MECHANICS;

CRACKS;

EID: 84880168386     PISSN: 16137736     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-37910-9_5     Document Type: Article

References (73)

1. Grambow, A.: Determination of Material Parameters for Filled Rubber Depending on Time, Temperature and Loading Condition. PhD thesis, Fakultät für Maschinenwesen, Rheinisch-Westfälische Technische Hochschule Aachen (2002)
2. Mooney, M.: A theory of large elastic deformation. Journal of Applied Physics 11, 582-592 (1940)
3. Yeoh, O.: Characterization of elastic properties of carbon-black-filled rubber vulcanizates. Rubber Chemistry and Technology 63, 792-805 (1990)
4. Arruda, E., Boyce, M.: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids 41, 389-412 (1993)
5. Miehe, C., Göktepe, S., Lulei, F.: A micro-macro approach to rubber-like materials. Part I: The non-affine micro-sphere model of rubber elasticity. Journal of the Mechanics and Physics of Solids 52, 2617-2660 (2004)
6. Marckmann, G., Verron, E.: Comparison of hyperelastic models for rubberlike materials. Rubber Chemistry and Technology 79, 835-858 (2006)
7. Kaliske, M., Heinrich, G.: An extended tube-model for rubber elasticity: Statistical-mechanical theory and finite element implementation. Rubber Chemistry and Technology 72, 602-632 (1999)
8. Dal, H., Kaliske, M.: Bergström-Boyce model for nonlinear finite rubber viscoelasticity: Theoretical aspects and algorithmic treatment for the FE method. Computational Mechanics 44, 809-823 (2009)
9. Behnke, R., Dal, H., Kaliske, M.: An extended tube model for thermoviscoelasticity of rubberlike materials: Parameter identification and examples. Proceedings in Applied Mathematics and Mechanics 11, 353-354 (2011)
10. Behnke, R., Dal, H., Kaliske, M.: An extended tube model for thermoviscoelasticity of rubberlike materials: Theory and numerical implementation. In: Jerrams, S., Murphy, N. (eds.) Constitutive Models for Rubber VII, pp. 87-92. CRC Press, Taylor & Francis Group (2011)
11. Kaliske, M., Zopf, C., Brüggemann, C.: Experimental characterization and constitutive modeling of the mechanical properties of uncured rubber. Rubber Chemistry and Technology 83, 1-15 (2010)
12. Dal, H., Kaliske, M., Zopf, C.: Theoretical and numerical modelling of unvulcanized rubber. In: Jerrams, S., Murphy, N. (eds.) Constitutive Models for Rubber VII, pp. 99-106. CRC Press, Taylor & Francis Group (2011)
13. Green, M., Tobolsky, A.: A new approach to the theory of relaxing polymeric media. The Journal of Chemical Physics 14, 80-92 (1946)
14. Doi, M., Edwards, S.F.: The Theory of Polymer Dynamics. Clarendon Press, Oxford (1986)
15. Bergström, J., Boyce, M.: Constitutive modeling of the large strain timedependent behavior of elastomers. Journal of the Mechanics and Physics of Solids 46, 931-954 (1998)
16. Reese, S., Govindjee, S.: A theory of finite viscoelasticity and numerical aspects. International Journal of Solids and Structures 35, 3455-3482 (1998)
17. Miehe, C., Keck, J.: Superimposed finite elastic-viscoelastic-plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation. Journal of the Mechanics and Physics of Solids 48, 323-365 (2000)
18. Miehe, C., Göktepe, S.: A micro-macro approach to rubber-like materials. Part II: The micro-sphere model of finite rubber viscoelasticity. Journal of the Mechanics and Physics of Solids 53, 2231-2258 (2005)
19. Cohen, A.: A Padé approximant to the inverse Langevin function. Rheologica Acta 30, 270-273 (1991)
20. Amin, A., Lion, A., Sekita, S., Okui, Y.: Nonlinear dependence of viscosity in modeling the rate-dependent response of natural and high damping rubbers in compression and shear: Experimental identification and numerical verification. International Journal of Plasticity 22, 1610-1657 (2006)
21. Dal, H.: Approaches to the Modeling of Inelasticity and Failure of Rubberlike Materials. Theory and Numerics. PhD thesis, Institut für Statik und Dynamik der Tragwerke, Technische Universität Dresden (2012)
22. Kaliske, M., Rothert, H.: Constitutive approach to rate-independent properties of filled elastomers. International Journal of Solids and Structures 35, 2057-2071 (1998)
23. Valanis, K.: A theory of viscoplasticity without a yield surface. Archives of Mechanics 23, 517-533 (1971)
24. Kilian, H., Strauss, M., Hamm, W.: Universal properties in fillerloaded rubbers. Rubber Chemistry and Technology 67, 1-16 (1994)
25. Netzker, C., Dal, H., Kaliske, M.: An endochronic plasticity formulation for filled rubber. International Journal of Solids and Structures 47, 2371-2379 (2010)
26. Besdo, D., Ihlemann, J.: A phenomenological constitutive model for rubberlike materials and its numerical applications. International Journal of Plasticity 19, 1019-1036 (2003)
27. Maugin, G.: Material Inhomogeneities in Elasticity. Chapman Hall, London (1993)
28. Gurtin, M.: Configurational Forces as Basic Concept of Continuum Physics. Springer, New York (2000)
29. Kienzler, R., Herrmann, G.: Mechanics in Material Space-with Application to Defect and Fracture Mechanics. Springer, Berlin (2000)
30. Morse, P.: Diatomic molecules according to the wave mechanics. II. Vibrational levels. Physical Review 34, 57-64 (1929)
31. Dal, H., Kaliske, M.: A micro-continuum-mechanical model for failure of rubber-like materials: Application to ageing-induced fracturing. Journal of the Mechanics and Physics of Solids 57, 1340-1356 (2009)
32. Treloar, L.: Stress-strain data for vulcanised rubber under various types of deformation. Transactions of the Faraday Society 40, 59-70 (1944)
33. Hamdi, A., Näit Abdelaziz, M., Äit Hocine, N., Heuillet, P., Benseddiq, N.: Fracture criterion of rubber-like materials under plane stress conditions. Polymer Testing 25, 994-1005 (2006)
34. Griffith, A.: The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London. Series A 221, 163-198 (1920)
35. Rice, J.: A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 35, 379-386 (1968)
36. Eshelby, J.: The elastic energy-momentum tensor. Journal of Elasticity 5, 321-335 (1975)
37. Netzker, C., Horst, T., Reincke, K., Behnke, R., Kaliske, M., Heinrich, G., Grellmann, W.: Analysis of stable crack propagation in filled rubber based on a global energy balance. International Journal of Fracture (2013), doi:10.1007/s10704-013-9816-5
38. Näser, B., Kaliske, M., Müller, R.: Material forces for inelastic models at large strains: Application to fracture mechanics. Computational Mechanics 40, 1005-1013 (2007)
39. Näser, B.: Zur numerischen Bruchmechanik dissipativer Materialien. PhD thesis, Institut für Statik und Dynamik der Tragwerke, Technische Universität Dresden (2009)
40. Behnke, R., Kaliske, M.: Computation of material forces for the thermomechanical response of dynamically loaded elastomers. Proceedings in Applied Mathematics and Mechanics 12, 299-300 (2012)
41. Mueller, R., Kolling, S., Gross, D.: On configurational forces in the context of the finite element method. International Journal for Numerical Methods in Engineering 53, 1557-1574 (2002)
42. Steinmann, P., Ackermann, D., Barth, F.: Application of material forces to hyperelastostatic fracture mechanics. II. Computational setting. International Journal of Solids and Structures 38, 5509-5526 (2001)
43. Liebe, T., Denzer, R., Steinmann, P.: Application of the material force method to isotropic continuum damage. Computational Mechanics 30, 171-184 (2003)
44. Menzel, A., Denzer, R., Steinmann, P.: On the comparison of two approaches to compute material forces for inelastic materials. Application to single-slip crystal-plasticity. Computer Methods in Applied Mechanics and Engineering 193, 5411-5428 (2004)
45. Zimmermann, D.: Material Forces in Finite Inelasticity and Structural Dynamics: Topology Optimization, Mesh Refinement and Fracture. PhD thesis, Institut für Mechanik (Bauwesen), Lehrstuhl I, Universität Stuttgart (2008)
46. Kaliske, M., Dal, H., Fleischhauer, R., Jenkel, C., Netzker, C.: Characterization of fracture processes by continuum and discrete modelling. Computational Mechanics 50, 303-320 (2012)
47. Hiermaier, S.: Structures under Crash and Impact. Springer, Berlin (2008)
48. Belytschko, T., Black, T.: Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 45, 601-620 (1999)
49. Neumann, J.: Anwendung von adaptiven Finite Element Algorithmen auf Probleme der Strukturdynamik. PhD thesis, Fakultät für Bauingenieur-, Geo-und Umweltwissenschaften, Institut für Mechanik, Universität Karlsruhe (2004)
50. Song, J.H., Wang, H., Belytschko, T.: A comparative study on finite element methods for dynamic fracture. Computational Mechanics 42, 239-250 (2008)
51. Dugdale, D.: Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 8, 100-104 (1960)
52. Barenblatt, G.I.: The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 7, 55-129 (1962)
53. Needleman, A.: A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics 54, 525-531 (1987)
54. Geißler, G.: The Cohesive Crack Tip Model within the Finite Element Method. Implementations, Enhancements, Applications. PhD thesis, Institut für Statik und Dynamik der Tragwerke, Technische Universität Dresden (2009)
55. Geißler, G., Kaliske, M.: Time-dependent cohesive zone modelling for discrete fracture simulation. Engineering Fracture Mechanics 77, 153-169 (2010)
56. Kaliske, M., Rothert, H.: Formulation and implementation of three-dimensional viscoelasticity at small and finite strains. Computational Mechanics 19, 228-239 (1997)
57. Geißler, G., Kaliske, M., Nase, M., Grellmann, W.: Peel process simulation of sealed polymeric film: Computational modelling of experimental results. Engineering Computations 24, 586-607 (2007)
58. Nase, M., Langer, B., Baumann, H., Grellmann, W., Geißler, G., Kaliske, M.: Evaluation and simulation of the peel behavior of polyethylene/polybutene-1 peel systems. Journal of Applied Polymer Science 111, 363-370 (2009)
59. Hillerborg, A., Modéer, M., Petersson, P.E.: Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research 6, 773-781 (1976)
60. Camacho, G., Ortiz, M.: Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures 33, 2899-2938 (1996)
61. Pandolfi, A., Ortiz, M.: Solid modeling aspects of three-dimensional fragmentation. Engineering with Computers 14, 287-308 (1998)
62. Pandolfi, A., Ortiz, M.: An efficient adaptive procedure for three-dimensional fragmentation simulations. Engineering with Computers 18, 148-159 (2002)
63. Papoulia, K., Sam, C.H., Vavasis, S.: Time continuity in cohesive finite element modeling. International Journal for Numerical Methods in Engineering 58, 679-701 (2003)
64. Wells, G., Sluys, L.: A new method for modelling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering 50, 2667-2682 (2001)
65. Pidaparti, R., Yang, T., Soedel, W.: Plane stress finite element prediction of mixed-mode rubber fracture and experimental verification. International Journal of Fracture 45, 221-241 (1990)
66. Gürses, E.: Aspects of Energy Minimization in Solid Mechanics: Evolution of Inelastic Microstructures and Crack Propagation. PhD thesis, Institut für Mechanik (Bauwesen), Lehrstuhl I, Universität Stuttgart (2007)
67. Kaliske, M., Ozenç, K., Dal, H.: Aspects of crack propagation in small and finite strain continua. In: Jerrams, S., Murphy, N. (eds.) Constitutive Models for Rubber VII, pp. 137-142. CRC Press, Taylor & Francis Group (2011)
68. Kaliske, M., Näser, B., Meiners, C.: Inelastic fracture mechanics for tire durability simulations. Tire Science and Technology 35, 239-250 (2007)
69. Nasdala, L., Wei, Y., Rothert, H., Kaliske, M.: Lifetime prediction of tires with regard to oxidative aging. Tire Science and Technology 36, 63-79 (2008)
70. Previati, G., Kaliske, M.: Crack propagation in pneumatic tires: Continuum mechanics and fracture mechanics approaches. International Journal of Fatigue 37, 69-78 (2012)
71. Näser, B., Kaliske, M., Dal, H., Netzker, C.: Fracture mechanical behaviour of visco-elastic materials: Application to the so-called dwell-effect. Zeitschrift für Angewandte Mathematik und Mechanik 89, 677-686 (2009)
72. Harbour, R., Fatemi, A., Mars, W.: The effect of a dwell period on fatigue crack growth rates in filled SBR and NR. Rubber Chemistry and Technology 80, 838-853 (2007)
73. Näser, B., Kaliske, M., Mars, W.: Fatigue investigation of elastomeric structures. Tire Science and Technology 38, 194-212 (2010)