Object-Oriented Programming Applied to the Finite Element Method Part II. Application to Material Behaviors

ABSTRACT This paper examines the application of C++ design patterns to the development of material constitutives equations to be used in finite element simulation softwares. All material behaviors use the same generic interface. Accordingly, the same governing principles can be applied to simple elasto-(visco)-plastic materials as well as single crystals, polycrystals and multiphased materials. As these models use numerous parameters, a generic optimization tools was also developed to adjust these parameters. Finally, a specific pre-processor can be used to quickly implement and test new material behaviors. The result (i.e., interface + optimizer + pre—processor) is an integrated approach to the development of new constitutive equations for structural computations.

[1]  G. Cailletaud A micromechanical approach to inelastic behaviour of metals , 1992 .

[2]  E. Kröner Zur plastischen verformung des vielkristalls , 1961 .

[3]  J. Mandel Generalisation de la theorie de plasticite de W. T. Koiter , 1965 .

[4]  P. Franciosi,et al.  The concepts of latent hardening and strain hardening in metallic single crystals , 1985 .

[5]  S. Ahzi,et al.  A self consistent approach of the large deformation polycrystal viscoplasticity , 1987 .

[6]  Rodney Hill,et al.  Continuum micro-mechanics of elastoplastic polycrystals , 1965 .

[7]  C. G. Broyden The Convergence of a Class of Double-rank Minimization Algorithms 2. The New Algorithm , 1970 .

[8]  Georges Cailletaud,et al.  Finite element analysis of the stress-strain behavior of single-crystal tubes , 1995 .

[9]  Thomas Bäck,et al.  Evolutionary Algorithms in Theory and Practice , 1996 .

[10]  J. Chaboche Constitutive equations for cyclic plasticity and cyclic viscoplasticity , 1989 .

[11]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[12]  G. Cailletaud,et al.  F. E. calculations of copper bicrystal specimens submitted to tension-compression tests , 1994 .

[13]  G. Cailletaud,et al.  Single Crystal Modeling for Structural Calculations: Part 2—Finite Element Implementation , 1991 .

[14]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[15]  U. F. Kocks,et al.  Latent hardening in aluminum , 1966 .

[16]  André Zaoui,et al.  An extension of the self-consistent scheme to plastically-flowing polycrystals , 1978 .

[17]  J. Hutchinson,et al.  Bounds and self-consistent estimates for creep of polycrystalline materials , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.