Nonlinear Regression Problem of Material Functions Identification for Porous Media Plastic Flow
A.A. AFIFI, S.P. AZEN, Statistical analysis. A computer oriented approach, Academic Press, New York 1979.
C.G. BOENDER, A.H.G. RINNOOY KAN, L. STROUGIE, G.T. TIMMER, A Stochastic method for global optimization, Mathematical Programming, 22, 125–140, 1982.
P.W. BRIDGMAN, Studies in large plastic flow and fracture, McGraw-Hill, 1952.
C.C. CHU, A. NEEDLEMAN, Void nucleation effects in biaxially stretched sheets, Trans. ASME, J. Engng. Materials and Technology, 102, 249–256, July 1980.
W. FINDEISEN, J. SZYMANOWSKI, A. WIERZBICKI, Theory and computational methods of optimization [in Polish], PWN, Warszawa 1977.
J.R. FISHER, Void nucleation in spheroidized steels during tensile deformation, Ph.D. Thesis, Brown University, June 1980.
R. FLETCHER, Practical methods of optimization, second edition, John Wiley & Sons, Chichester 1987.
A.A. GOLDSTEIN, On steepest descent, SIAM J. Control, 3, 147–151, 1965.
A.L. GURSON, Continuum theory of ductile rupture by void nucleation and growth. Part 1. Yield criteria and flow rules for porous ductile media, J. Engng. Materials and Technology, Trans. of the ASME, 99, 2–15, 1977.
R. HILL, Mathematical plasticity, Oxford Press, 1950.
K. LEVENBERG, A Method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math., 2, 164–168, 1944.
D.W. MARQUARDT, An algorithm for least squares estimation of nonlinear parameters, SIAM Journal on Applied Mathematics, 11, 431–441, 1963.
A. NEEDLEMAN, J.R. RICE, Limits to ductility set by plastic flow localization, D.P. KOISTINEN, N. M. WANG, [Eds.], Mechanics of Sheet Metal Forming, 237–267, Plenum, New York 1978.
Z. NOWAK, A. STACHURSKI, Global optimization in material functions identification for voided media plastic flow, submitted for publication in CAMES, 2002.
P. PERZYNA, Internal state variable description of dynamic fracture of ductile solids, Int. J. Solids Structure, 22, 797–818, 1986.
P. PERZYNA, Z. NOWAK, Evolution equation for the void fraction parameter in necking region, Arch. Mech., 39, No. 1–2, 73–84, 1987.
W.H. PRESS, S.A. TEUKOLSKY, W.T. VETTERLING, B.P. FLANNERY, Numerical recipes in C: The art of scientific computing, Cambridge University Press, Cambridge 1993.
J.W. RUDNICKI, J.R. RICE, Conditions for the localization of deformation in pressure–sensitive delatant materials, Journal Mech. Phys. Solids, 23, 371–394, 1975.
M. SAJE, J. PAN, A. NEEDLEMAN, Void nucleation effects on shear localization in porous plastic solids, Int. J. Fracture, 19, 163, 1982.
A. STACHURSKI, A.P. WIERZBICKI, Introduction to optimization [in Polish], Publishing House of the Warsaw University of Technology, Warsaw 1999.
A. TÖRN, A. ŽILINSKAS, Global optimization, Springer Verlag, Berlin, Heidelberg 1989. Received December 29, 2000.