Abstract
An object-oriented approach to the analysis and design of metal forming and directional solidification processes is presented. A number of specific ideas are introduced on how a deformation or a solidification process can be partitioned into subproblems that can be independently developed and tested in the form of class hierarchies. Class development based on mathematical and/or physical arguments is emphasized. General ideas are provided to demonstrate that an OOP approach to the FEM modeling and design of material processes can lead to efficient simulators that are easily maintainable and expandable. A metal forming example is presented to demonstrate the ability of the deformation simulator to handle the analysis of industrial metal forming processes. Also, a design directional solidification example is presented to demonstrate the substantial benefits of using OOP techniques for the design of processes with a desired solidification morphology.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
ABAQUS. Reference Manual. Hibbit, Karlsson and Sorensen Inc., 100 Medway Street, Providence, RI, 02906–4402, 1989.
O. M. Alifanov. Inverse Heat Transfer Problems. Springer-Verlag, Berlin, 1994.
N. Aravas. On the numerical integration of a class of pressure-dependent plasticity models. Int. J. Numer. Methods Engr. 24 (1987) 1395–1416.
E. Arge, A. M. Bruaset and H. P. Langtangen (edts.). Modern Software Tools for Scientific Computing. Birkhäuser, Boston, 1997.
S. Badrinarayanan and N. Zabaras. A sensitivity analysis for the optimal design of metal forming processes. Comp. Methods Appl. Mech. Engr. 129 (1996) 319–348.
J. J. Barton and L. R. Nackman. Scientific and Engineering C++. Addison-Wesley, New York, 1994.
P. Bomme. Intelligent Objects in Object-Oriented Engineering Environments. Ph.D. Thesis, École Polytechnique F¨¦d¨¦rale de Lausanne, Th¨¨se No. 1763, 1998.
A. N. Brooks and T. J. R. Hughes. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comp. Methods App/. Mech. Engr. 32 (1982) 199–259.
S. B. Brown, K. H. Kim and L. Anand. An internal variable constitutive model for hot working of metals. Int. J. Plasticity 5 (1989) 95–130.
J. Budiansky. Thermal and thermoelastic properties of isotropic composites. J. Composite Materials 4 (1970) 286–295.
H. S. Carslaw and J. C. Jaeger. Conduction of Heat in Solids. Oxford University Press, 2nd Ed., New York, 1959.
M. Daehlen and A. Tveito (edts.). Numerical Methods and Software Tools in Industrial Mathematics. Birkäuser, Boston, 1997.
M. S. Engleman. FIDAP, v. 7.52. Fluid Dynamic International, Incorporated, 1996.
A. L. Gurson. Continuum theory of ductile rupture by void nucleation and growth: Part 1 - Yield criteria and flow rules for a porous ductile media. J. Engr. Mat. Techn. 99 (1977) 2–15.
W. Kurz and D. J. Fisher. Fundamentals of Solidification. Trans Tech Publications Ltd, Switzerland, 1989.
H. P. Langtangen. Computational Partial Differential Equations - Numerical Methods and Diffpack Programming. Springer-Verlag, New York, 1999.
T. A. Laursen and J. C. Simo. On the formulation and numerical treatment of finite deformation frictional contact problems. Nonlinear Computational Mechanics - State of the Art, (edts.) P. Wriggers and W. Wager. Springer Verlag, Berlin, (1991) 716–736.
D. G. Luenberger. Optimization by vector space methods (Series in Decision and Control). J. Wiley and Sons, New York, 1997.
A.M. Lush. Computational procedures for finite element analysis of hot working. Ph.D. Thesis, MIT, 1990.
A. M. Lush. Thermo-mechanically-coupled finite element analysis of hot-working using an implicit constitutive time integration scheme. Numerical Methods in Industrial Forming Processes (edts. J.-L. Chenot, R.D. Wood and O.C. Zienkiewicz) (1992) 281–286.
R. I. Mackie. Object oriented programming of the finite element method. Int. J. Numer. Methods Engr. 35 (1992) 425–436.
R. I. Mackie. Using objects to handle complexity in FE software. Engineering with Computers 13 (1997) 99–111.
G. I. Marchuck. Adjoint Equations and Analysis of Complex Systems. Kluwer Academic Publishers, Boston, 1995.
B. Moran, M. Ortiz and C. F. Shih. Formulation of implicit finite element methods for multiplicative finite deformation plasticity. Int. J. Numer. Methods Engr. 29 (1990) 483–514.
R. Sampath and N. Zabaras. An object-oriented implementation of adjoint techniques for the design of complex continuum systems. Int. J. Numer. Methods Engr., submitted for publication.
R. Sampath and N. Zabaras. An object oriented implementation of a front tracking finite element method for directional solidification processes. Int. J. Numer. Methods Engr. 44(9) (1999) 1227–1265.
R. Sampath and N. Zabaras. Inverse thermal design and control of solidification processes in the presence of a strong magnetic field. J. Comp. Physics, submitted for publication.
R. Sampath and N. Zabaras. A diffpack implementation of the Brooks/Hughes Streamline-upwind/Petrov-Galerkin FEM formulation for the incompressible Navier-Stokes equations. Research Report MM-97–01, Sibley School of Mechanical and Aerospace Engineering, Cornell University,http://www.mae.cornell.edu/research/zabaras1997
R. Sampath and N. Zabaras. Finite element simulation of buoyancy driven flows using an object-oriented approach. Research Report MM-97–02, Sibley School of Mechanical and Aerospace Engineering, Cornell University http://www.mae.cornell.edu/research/zabaras,1997.
R. Sampath and N. Zabaras. FEM simulation of double diffusive convection using an object-oriented approach. Research Report MM-97–03, Sibley School of Mechanical and Aerospace Engineering, Cornell University http://www.mae.cornell.edu/research/zabaras,1997.
R. Sampath and N. Zabaras. FEM simulation of alloy solidification in the presence of magnetic fields. Research Report MM-97–04, Sibley School of Mechanical and Aerospace Engineering, Cornell University http://www.mae.cornell.edu/research/zabaras,1997.
R. Sampath and N. Zabaras. Design and object-oriented implementation of a preconditioned-stabilized incompressible Navier-Stokes solver using equal-order interpolation velocity-pressure elements. Research Report MM-99–01, Sibley School of Mechanical and Aerospace Engineering,Cornell Universityhttp://www.mae.cornell.du/research/zabaras, 1999.
J. C. Simo and C. Miehe. Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation. Comp. Methods Appl. Mech. Engr.98 (1992) 41–104.
A. Srikanth and N. Zabaras. A computational model for the finite element analysis of thermoplasticity coupled with ductile damage at finite strains.Int. J. Num. Meth. Eng.,in press.
N. Zabaras. Adjoint methods for inverse free convection problems with application to solidification processes. Computational Methods for Optimal Design and Control (edts. J. Borggaard, E. Cliff, S. Schreck and J. Burns). Birkäuser Series in Progress in Systems and Control Theory, Birkäuser (1998) 391–426.
A. Srikanth and N. Zabaras. Preform design and shape optimization in metal forming. Comp. Methods Appl. Mech. Engr., submitted for publication.
T.E. Tezduyar. Stabilized finite element formulations for incompressible flow computations. Advances in Applied Mechanics 28 (1991) 1–44.
T. E. Tezduyar, M. Behr and J. Liou. A new strategy for finite element computations involving moving boundaries and interfaces - the deformingspatial-domain/space-time procedure: I. The concept and the preliminary tests. Comp. Meth. Appl. Mech. Engr. 94 (1992) 339–351.
T. E. Tezduyar, M. Behr, S. Mittal and A. A. Johnson. Computation of unsteady incompressible flows with the finite element method - space-time formulations, iterative strategies and massively parallel implementations. New Methods in Transient Analysis (edts. P. Smolinski, W. K. Liu, G. Hulbert and K. Tamma, ASME, New York) AMD 143 (1992) 7–24.
V. Tvergaard and A. Needleman. Elastic-Viscoplastic analysis of ductile fracture. Finite Inelastic Deformations - Theory and Applications, (edts. D. Bedso and E. Stein). IUTAM symposium Hannover, Germany (1991) 3–14.
G. Weber and L. Anand. Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic-viscoplastic solids.Comp. Methods Appl. Mech. Engr., 79 (1990) 173–202.
G. Yang and N. Zabaras. The adjoint method for an inverse design problem in the directional solidification of binary alloys. J. Comp. Phys. 140(2) (1988) 432–452.
G. Yang and N. Zabaras. An adjoint method for the inverse design of solidification processes with natural convection. Int. J. Num. Meth. Eng. 42 (1998) 1121–1144.
N. Zabaras, Y. Bao, A. Srikanth and W. G. Frazier A continuum sensitivity analysis for metal forming processes with application to die design problems.Int. J. Numer. Methods Engr., submitted for publication.
N. Zabaras and T. Hung Nguyen. Control of the freezing interface morphology in solidification processes in the presence of natural convection. Int. J. Num. Meth. Eng. 38 (1995) 1555–1578.
N. Zabaras and A. Srikanth. An object oriented programming approach to the Lagrangian FEM analysis of large inelastic deformations and metal forming processes. Int. J. Num. Meth. Eng., in press.
N. Zabaras and G. Yang. A functional optimization formulation and FEM implementation of an inverse natural convection problem. Comp. Meth. Appl. Mech. Eng. 144(3–4) (1997) 245–274.
N. Zabaras and A. Srikanth. Using objects to model finite deformation plasticity. Engineering with Computers, in press.
A. Zavaliangos, L. Anand, B. F. von Turkovich. Deformation processing. Annals of the CIRP 40 (1991) 267–271.
A. Zavaliangos and L. Anand. Thermal aspects of shear localization in microporous viscoplastic solids. Int. J. Numer. Methods Engr. 33 (1992) 595–634.
Z. L. Zhang. On the accuracy of numerical integration algorithms for Gurson-based pressure dependent elastoplastic constitutive models. Comp. Methods Appl. Mech. Engr. 121 (1995) 15–28.
Z. L. Zhang. Explicit consistent tangent moduli with a return mapping algorithm for pressure-dependent elastoplasticity models. Comp. Methods Appl. Mech. Engr. 121 (1995) 29–44.
T. Zimmermann, Y. Dubois-P¨¨lerin and P. Bomme. Object-oriented finite element programming: I Governing principles. Comp. Methods Appl. Mech. Engr. 98 (1992) 291–303.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zabaras, N. (2000). An Object-Oriented Approach to the Finite Element Modeling and Design of Material Processes. In: Langtangen, H.P., Bruaset, A.M., Quak, E. (eds) Advances in Software Tools for Scientific Computing. Lecture Notes in Computational Science and Engineering, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57172-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-57172-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66557-1
Online ISBN: 978-3-642-57172-5
eBook Packages: Springer Book Archive