Large deformation analysis of rubber based on a reproducing kernel particle method

Computational Mechanics

Volumn 19, Issue 3, 1997, Pages 211-227

  Chen, J S ^a   Pan, C ^a   Wu, C T ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DEFORMATION; ELASTICITY; LAGRANGE MULTIPLIERS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; VARIATIONAL TECHNIQUES;

GALERKIN APPROXIMATIONS; REPRODUCING KERNEL PARTICLE METHOD (RKPM);

RUBBER;

EID: 0031074562     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004660050170     Document Type: Article

References (37)

1. Bercovier, M. (1978): Perturbation of mixed variational problems, application to mixed finite element methods. R. A. I. R. O. Num. Anal. 12: 211-236
2. Belytschko, T.; Lu Y. Y.; Gu, L. (1994a): Element-free Galerkin methods Int. J. Numer. Meth. Eng. 37: 229-256
3. Belytschko, T. (1994b): Are finite elements passé ? USACM Bulletin 7: 4-7
4. Belytschko, T.; Gu, L.; Lu, Y. Y. (1994c): Fracture and crack growth by EFG method, Modeling Simul. Mater. Sci. Eng., 2: 519-534
5. Belytsehko, T.; Organ, D.; Krongarz, Y. (1995): A coupled finite element-element-free Galerkin method, Comput. Mech. 177: 186-195
6. Chang, T. Y. P.; Saleeb, A.-F.; Li, G. (1991): Large strain analysis of rubber-like materials based on a perturbed lagrangian variational Principle. Comput. Mech. 8: 221-233
7. Charrier, P.; Dacorogna, B.; Hanouzet, B.; Laborde, P. (1988): An existence theorem for slightly compressible materials in nonlinear elasticity. SIAM, J. Math. Anly. 19: 70-85
8. Chen, J.-S.; Satyamurthy, K.-S.; Hirschfeit, L.-R. (1994): Consistent finite element procedures for nonlinear rubber elasticity with a higher order strain energy function. Comput. & Struct. 50: 715-727
9. Chen, J.-S.; Pan, C. (1995a): A pressure projection method for nearly incompressible rubber hyperelasticity, Part I: Theory, in press, Journal of Applied Mechanics
10. Chen, J.-S.; Wu, C.-T.; Pan, C. (1995b): A pressure projection method for nearly incompressible rubber hyperelasticity, Part II: applications, in press, Journal of Applied Mechanics
11. Chen, J.-S.; Han, W.; Wu, C.-T.; Duan, W. (1995c): On the perturbed Lagrange formulation for nearly incompressible and incompressible hyperelasticity, in press, Comput. Meth. Appl. Mech. Engng
12. Chen, J.-S.; Pan, C.; Chang, T.-Y.-P. (1995d): On the control of pressure oscillation in bilinear-displacement constant-pressure element. 128: 137-152
13. Gent, A.-N.; Lindley, P.-B. (1959): The compression of bonded rubber blocks. Proc. Inst. Mech. Engrs. 173: 111-122
14. Herrmann, L.-R. (1965): Elasticity equations for incompressible and nearly incompressible materials by a variational theorem. AIAA Jnl. 3: 1896-1900
15. Johnson, G.-R.; Peterson, E.-H.; Stryrk, R.-A. (1993): Incorporation of an SPH option into the EPIC code for a wide range of high velocity impact computations, preprint
16. Key, S.-W. (1969): A variational principle for incompressible and nearly incompressible anisotropic elasticity. Int. J. Solids Struct. 5: 951-964
17. Libersky, L.-D.; Petschek, A.-G.; Carney, T.-C.; Hipp, J.-R.; Allahdadi, F.A. (1993): High strain Lagrangian hydrodynamics. J. Comp. Phys. 109: 67-75
18. Liu, W.-K.; Ong, J.-S.-J.; Uras, R.-A. (1985): Finite element stabilization matrices - A unification approach. Comput. Meth. Appl. Mech. Engng. 53: 13-46
19. Liu, W.-K.; Belytschko, T.; Chen, J.-S. (1988): Nonlinear versions of flexurally superconvergent elements. Comput. Meth. Appl. Mech. Engng. 71: 241-256
20. Liu, W.-K.; Jun, S.; Li, S.; Adee, J.; Belytschko, B. (1995a): Reproducing kernel particle methods for structural dynamics. Int. J. Numer. Meth. Eng. 38: 1655-1679
21. Liu, W.-K.; Jun, S.; Zhang, Y.-F. (1995b): Reproducing kernel particle methods. Int J. Numer. Meth. Fluids. 20: 1081-1106
22. Liu, W.-K. (1995c): An introduction to wavelet reproducing kernel particle methods. USACM Bulletin. 8: 3-16
23. Liu, W.-K.; Chen, Y. (1995d): Wavelet and multi-scale reproducing kernel particle methods. Int. J. Numer. Meth. Fluids. 21: 901-931
24. Liu, W.-K.; Li, S.; Belytschko, T. (1995c): Moving least square kernel Galerkin method (I) methodology and convergence, to appear, Comput, Meth. Appl. Mech. Engng
25. Liu, W.-K.; Chen, Y.; Jun, S.; Chen, J.-S.; Belytschko, T.; Pan, C.; Uras, R.-A.; Chang, C.-T. (1996a): Overview and applications of the reproducing kernel particle methods. Archives of Computational Methods in Engineering State of Art Reviews. 3: 3-80
26. Liu, W.-K.; Chen, Y.; Chang, R.-A.; Chang C.-T. (1996b): Generalized multiple scale reproducing kernel particle methods, to appear, Comput. Meth. Appl. Mech. Engng.
27. Lu, Y.-Y.; Belytschko, T.; Gu, L. (1994): A new implementation of the element free Galerkin method. Comput. Meth. Appl. Mech. Engng. 113: 397-414
28. Malkas, D.-S.; Hughes, T.-J.-R. (1978): Mixed finite element methods-reduced and selective integration techniques: a unification of concept. Comput. Meth. Appl. Mech. Engng. 15: 63-81
29. Monaghan, J.-J. (1982): Why particle methods work. SIAM J. Sci. Stat. Comput. 3: 422-433
30. Monaghan, J.-J. (1988): An introduction to SPH. Computer Physics Communications, 48. 89-96
31. Mooney, M (1940): A theory of large elastic deformation. J. Appl. Phys. 11: 582-592
32. Penn, R.-W. (1970): Volume changes accompanying the extension of rubber. Trans. Soc. Rheo. 14: 4, 509-517
33. Rivlin, R.-S. (1956): Rheology theory and applications, ed. F. R. Eirich, 1, Chap. 10, 351-385, Academic Press, New York, NY
34. Tong, P. (1969): An assumed stress hybrid finite element method for an incompressible and nearly-incompressible material Int. J. Solids Struct. 5: 455-461
35. Tseng, N.-T.; Satyamurthy, K.; Chang, J.-P. (1987), Nonlinear finite element analysis of rubber based products, Rubber Division, Montreal, Quebec, May 26-29
36. Yeoh, O.-H. (1990): Characterization of elastic properties of carbon black filled rubber vulcanizates. Rubb. Chem. Technol. 63: 792-805
37. Yeoh, O.-H. (1993): Some forms of the strain energy function for rubber. Rubb. Chem. Technol. 66: 754-771