Multiscale modeling of material failure: From atomic bonds to elasticity with energy limiters

International Journal for Multiscale Computational Engineering

Volumn 6, Issue 5, 2008, Pages 393-410

  Volokh, Konstantin Y ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Bonds; Elasticity; Energy limiters; Material failure; Multiscale modeling; Softening

Indexed keywords

BRITTLE FRACTURE; CONSTITUTIVE MODELS; ELASTICITY; STRAIN; TISSUE;

BONDS; ENERGY LIMITERS; MATERIAL FAILURE; MULTISCALE MODELING; SOFTENING;

MATERIALS;

EID: 62749093699     PISSN: 15431649     EISSN: None     Source Type: Journal    
DOI: 10.1615/IntJMultCompEng.v6.i5.20     Document Type: Article

References (41)

1. Barenblatt, G. I., The Formation of Equilibrium Cracks during Brittle Fracture. General Ideas and Hypotheses: Axially-Symmetric Cracks. J. Appl. Math. Mech. 23:622-636, 1959.
2. Dugdale, D. S., Yielding of Steel Sheets Containing Slits. J. Mech. Phys. Solids 8:100-104, 1960.
3. Rice, J. R., and Wang, J. S., Embrittlement of Interfaces by Solute Segregation. Mater. Sci. Eng. A 107:23-40, 1989.
4. Tvergaard, V., and Hutchinson, J. W., The Relation between Crack Growth Resistance and Fracture Process Parameters in Elastic-Plastic Solids. J. Mech. Phys. Solids 40:1377-1397, 1992.
5. Xu, X. P., and Needleman, A., Numerical Simulations of Fast Crack Growth in Brittle Solids, J. Mech. Phys. Solids 42:1397-1434, 1994.
6. Camacho, G. T., and Ortiz, M., Computational Modeling of Impact Damage in Brittle Materials. I. J. Solids Struct. 33:2899-2938, 1996.
7. Needleman, A., A Continuum Model for Void Nucleation by Inclusion Debonding. J. Appl. Mech. 54:525-531, 1987.
8. De Borst, R., Some Recent Issues in Computational Failure Mechanics. Int. J. Numer. Meth. Eng. 52:63-95, 2001.
9. Belytschko, T., Moes, N., Usiu, S., and Parimi, C., Arbitrary Discontinuities in Finite Elements. Int. J. Num. Meth. Eng. 50:993-1013, 2001.
10. Kachanov, L. M., Time of the Rupture Process under Creep Conditions. Izvestiia Akademii Nauk SSSR, Otdelenie Teckhnicheskikh Nauk. 8:26-31, 1958.
11. Rabotnov, Y. N., On the Equations of State for Creep. In Progress in Applied Mechanics. Praeger Anniversary Volume. Macmillan, New York, 1963.
12. Kachanov, L. M., Introduction to Continuum Damage Mechanics. Martinus Nijhoff, Dortrecht, 1986.
13. Krajcinovic, D., Damage Mechanics. North Holland Series in Applied Mathematics and Mechanics. Elsevier, New York, 1996.
14. Skrzypek, J., and Ganczarski, A., Modeling of Material Damage and Failure of Structures. Springer, Berlin, 1999.
15. Lemaitre, J., and Desmorat, R., Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer, Berlin, 2005.
16. Gao, H., and Klein, P., Numerical Simulation of Crack Growth in an Isotropic Solid with Randomized Internal Cohesive Bonds. J. Mech. Phys. Solids. 46:187-218,1998.
17. Klein, P., and Gao, H., Crack Nucleation and Growth as Strain Localization in a Virtual-Bond Continuum. Eng. Fract. Mech. 61:21-48, 1998.
18. Volokh, K. Y., Nonlinear Elasticity for Modeling Fracture of Isotropic Brittle Solids. J. Appl. Mech. 71:141-143,2004.
19. Volokh, K. Y., Softening Hyperelasticity for Modeling Material Failure: Analysis of Cavitation in Hydrostatic Tension. Int. J. Solids Struct. 44:5043-5055, 2007.
20. Volokh, K. Y., Hyperelasticity with Softening for Modeling Materials Failure. J. Mech. Phys. Solids 55:2237-2264, 2007.
21. Werner, J. H., Statistical Mechanics of Elasticity. John Wiley, New York, 1983.
22. Tadmor, E. B., Ortiz, M., and Phillips, R., Quasicontinuum Analysis of Defects in Solids. Philos. Mag. 73:1529-1563, 1996.
23. Klein, P., and Gao, H., Study of Crack Dynamics using the Virtual Internal Bond Method. In Multiscale Deformation and Fracture in Materials and Structures. Kluwer, Dordrecht, 275-309, 2000.
24. Volokh, K. Y., and Vorp, D. A., A Model of Growth and Rupture of Abdominal Aortic Aneurysm. J. Biomech. 41:1015-1021, 2008.
25. Raghavan, M. L., and Vorp, D. A., Toward a Biomechanical Tool to Evaluate Rupture Potential of Abdominal Aortic Aneurysm: Identification of a Finite Strain Constitutive Model and Evaluation of its Applicability. J. Biomech. 33:475-482, 2000.
26. Volokh, K. Y., Fung's Arterial Model Enhanced with a Failure Description. Mol. Cell. Biomech. 5:207-216, 2008.
27. Vaishnav, R. N., Young, J. T., and Patel, D. J., Distribution of Stresses and of Strain-Energy Density through the Wall Thickness in a Canine Aortic Segment. Cir. Res. 32:577-583, 1973.
28. Rachev, A., and Greenwald, S. E., Residual Stresses in Conduit Arteries. J. Biomech. 36:661-670, 2003.
29. Volokh, K. Y., Stresses in Growing Soft Tissues. Acta Biomater. 2:493-504, 2006.
30. Fung, Y. C., Biomechanics: Motion, Flow, Stress, and Growth. Springer, New York, 1990.
31. Fung, Y. C., Biomechanics: Mechanical Properties of Living Tissues, 2nd ed. Springer, New York, 1993.
32. Volokh, K. Y., Prediction of Arterial Failure Based on a Microstructural Bi-Layer Fiber-Matrix Model with Softening. J. Biomech. 41:447-453, 2008.
33. Volokh, K. Y., and Trapper, P., Fracture Toughness from the Standpoint of Softening Hyperelasticity. J. Mech. Phys. Solids 56:2459-2472, 2008.
34. Trapper, P., and Volokh, K. Y., Cracks in rubber. Int. J. Solids Struct. 45:6034-6044, 2008.
35. Griffith, A. A., The Phenomena of Rupture and Flow in Solids. Philos. Trans. R. Soc. London, Ser. A 221:163-198, 1921.
36. Mullin, T., and Kerswell, R. R., Eds. Laminar Turbulent Transition and Finite Amplitude Solu- tions, Proceedings of the UITAM Symposium, Bristol, UK. Springer, Dordrecht, 2005.
37. Landau, L. D., and Lifshitz, E. M., Fluid Mechanics. Pergamon Press, Oxford, UK, 1987.
38. Batchelor, G. K., An Introduction to Fluid Dynamics. Cambridge University Press, New York, 2000.
39. Drazin, P. G., Introduction to Hydrodynamic Stability. Cambridge University Press, New York, 2002.
40. Schmid, P. J., and Henningson, D. S., Stability and Transition in Shear Flows. Springer, New York, 2001.
41. Romanov, V A., Stability of Plane-Parallel Couette Flow. Funct. Anal. Appl. 7:137-146, 1973.