Adaptivity and convergence in the Voronoi cell finite element model for analyzing heterogeneous materials

Computer Methods in Applied Mechanics and Engineering

Volumn 185, Issue 1, 2000, Pages 37-74

  Moorthy, Suresh ^a   Ghosh, Somnath ^a  

^a Ohio State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPOSITE MICROMECHANICS; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; ERROR CORRECTION; FUNCTIONS; KINEMATICS; MATHEMATICAL MODELS; MICROSTRUCTURE; POROUS MATERIALS; PROBLEM SOLVING; STRESS ANALYSIS;

VORONOI CELL FINITE ELEMENT MODEL;

FINITE ELEMENT METHOD;

EID: 0033731257     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00349-7     Document Type: Article

References (39)

1. Moorthy S., Ghosh S. A model for analysis of arbitrary composite and porous microstructures with Voronoi cell finite elements. Int. J. Numer. Meth. Engrg. 39:1996;2363-2398.
2. Ghosh S., Moorthy S. Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi cell finite element method. Comp. Meth. Appl. Mech. Engrg. 121:1995;373-409.
3. Ghosh S., Liu Y. Voronoi cell finite element method for micropolar thermo-elastic heterogeneous materials. Int. J. Numer. Meth. Engrg. 38(8):1995;1361-1398.
4. Moorthy S. The Voronoi cell finite element method for response and damage analysis of arbitrary heterogeneous media. 1997;Ph.D. Dissertation, The Ohio-State University, Columbus.
5. Ghosh S., Moorthy S. Particle fracture simulation in nonuniform microstructures of metal-matrix composites. Acta Mater. 46(3):1998;965-982.
6. Moorthy S., Ghosh S. A Voronoi cell finite element model for particle cracking in composite materials. Comp. Meth. Appl. Mech. Engrg. 151:1998;377-400.
7. Ghosh S., Mukhopadhyay S.N. A two-dimensional automatic mesh generator for finite element analysis of random composites. Comput. Struct. 41:1991;245-256.
8. Finot M., Shen Y.-L., Needleman A., Suresh S. Micromechanical modeling of reinforcement fracture in particle reinforced-matrix composites. Metall. Trans. A. 25:1994;2403-2420.
9. Brockenbrough J.R., Suresh S., Weinecke W.A. Deformation of metal-matrix composites with continuous fibers geometrical effects of fiber distribution and shape. Acta Metall. Mater. 39:1991;735-752.
10. Christman T., Needleman A., Suresh S. An experimental and numerical study of deformation in metal-ceramic composites. Acta Metall. Mater. 37:1989;3029-3050.
11. Ghosh S., Nowak Z., Lee K. Quantitative characterization and modeling of composite microstructures by Voronoi cells. Acta Mater. 45(6):1997;2215-2234.
12. Ghosh S., Nowak Z., Lee K. Tessellation based computational methods in characterization and analysis of heterogeneous microstructures. Comp. Sci. Tech. 57:1997;1187-1210.
13. Ghosh S., Lee K., Moorthy S. Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method. Int. J. Solids Struct. 32(1):1995;27-62.
14. Ghosh S., Lee K., Moorthy S. Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model. Comp. Meth. Appl. Mech. Engrg. 132:1996;63-116.
15. K. Lee, S. Moorthy, S. Ghosh, Multiple scale computational model for damage in composite materials, Comp. Meth. Appl. Mech. Engrg., 172 (1999) 175-201.
16. J.T. Oden, L. Demkowicz, T. Strouboulis, P. Devloo, in: I. Babuska, O.C. Zienkiewicz, J. Gago, E.R. Oliveria (Eds.), Adaptive Methods for Problems in Solid and Fluid Mechanics, Accuracy Estimates and Adaptive Refinements in Finite Element Computations, Wiley, New York, 1986, pp. 249-280.
17. Ainsworth M., Craig A. A posteriori error estimators in the finite element method. Numer. Math. 60:1992;429-463.
18. Ainsworth M., Oden J.T. A procedure for a posteriori error estimation for. h-p finite element methods Comp. Meth. Appl. Mech. Engrg. 101:1992;73-96.
19. Oden J.T., Wu W., Ainsworth M. An a posteriori error estimate for finite element approximations of the Navier Stokes equations. Comp. Meth. Appl. Mech. Engrg. 111:1994;185-202.
20. Babuska I., Rheinbolt W.C. Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15(4):1978;736-754.
21. Babuska I., Plank L., Rodriguez R. Quality assessment of the a posteriori error estimation in finite elements. Finite Elements in Anal. Design. 11:1991;285-305.
22. O.C. Zienkiewicz, J.Z. Zhu, The superconvergent patch recovery and aposteriori error estimates, Part I. The recovery techniques. Part 2. Error estimates and adaptivity, Int. J. Numer. Meth. Engrg. 33 (1992) 1365-1382.
23. Babuska I., Strouboulis T., Mathur A., Upadhyay C.S. Pollution error in the h-version of the finite element method and the local quality of a posteriori error estimators. Finite Elements in Anal. Design. 17:1994;273-321.
24. I. Babuska, T. Strouboulis, C.S. Upadhyay, S.K. Gangaraj, A posteriori estimation and adaptive control of the pollution error in the h -version of the finite method, CMC Report No. 94-06, August 1994.
25. J.T. Oden, Y. Feng, Local and pollution error estimation for finite element approximations of elliptic boundary value problems, TICAM Report 95-03, The University of Texas, 1995.
26. W-M. Xue, S.N. Atluri, Existence and stability and discrete BB and rank conditions for general mixed-hybrid finite elements in elasticity, in: R.L. Spilker, K.W. Reed (Eds.), Hybrid and Mixed Finite Element Methods ASME-AMD (13), 1985, pp. 91-112.
27. Xue W-M., Karlovitz L.A., Atluri S.N. On the existence and stability conditions for mixed-hybrid finite element solutions based on Reissner's variational principle. Int. J. Solids Struct. 21(1):1985;97-116.
28. Ying L-A., Atluri S.N. A hybrid finite element method for Stokes flow: Part II: stability and convergence studies. Comp. Meth. Appl. Mech. Engrg. 36:1983;39-60.
29. Babuska I. The finite element method with Lagrange multipliers. Numer. Math. 20:1973;179-192.
30. Babuska I., Oden J.T., Lee J.K. Mixed-hybrid finite element approximations of second order elliptic boundary value problems, Part I. Comp. Meth. Appl. Mech. Engrg. 11:1977;175-206.
31. F. Brezzi, On the existence uniqueness and approximation of saddle-point problems arising from Lagrange Multipliers, R.A.I.R.O 8-R2, 1974, pp. 129-151.
32. Reddy J.N., Oden J.T. Mathematical theory of mixed finite element approximations. Quart. Appl. Math. 33:1975;255-280.
33. J.K. Lee, Convergence of mixed-hybrid finite element models, Ph.D. Dissertation, University of Texas, Austin, 1976.
34. Muskhelishvili N.I. Some Basic Problems in the Mathematical Theory of Elasticity. 1965;P. Nordhoff, Netherlands.
35. Savin G. Stress Concentrations Around Holes. 1951;Pergamon Press, Oxford.
36. Timoshenko S.P., Goodier J.N. Theory of Elasticity. 1970;McGraw-Hill, New York.
37. Pagano N.J., Rybicki E.F. On the significance of effective modulus solutions for fibrous composites. J. Comp. Mater. 8:1974;214-228.
38. M. Kofler, Maple Version 5 Release 3: An Introduction and Reference, Addison-Wesley, Reading, MA, 1997.
39. ANSYS User's Manual, Version 5.3, Swanson Analysis Systems Inc.