The continuum sensitivity method for the computational design of three-dimensional deformation processes

Although simulation of metal forming processes using modern computational tools has reached an advanced stage, there is still a great need to develop computational techniques for process design. In this work, the continuum sensitivity method (CSM) is extended to three-dimensions (3D) to accurately compute sensitivity fields and in particular changes in the design objectives as a result of infinitesimal perturbations to the design parameters. CSM involves differentiation of the governing field equations of the direct problem (constitutive, contact and kinematic problems) with respect to the design variables and development of the weak forms for the corresponding sensitivity equations. The present 3D developments include a novel regularized approach to the contact sensitivity problem that addresses the non-differentiability of the contact constraints. The computed sensitivity fields are used in a gradient-based optimization framework for process design (optimization) in 3D metal forming applications. A typical design problem at each optimization iteration involves simultaneous solution of a direct problem and a number of sensitivity problems corresponding to each of the design variables. Relevant 3D design problems related to preform and die design for desired properties in the final product are considered highlighting the features and potential of the metal forming design simulator developed.

[1]  Tod A. Laursen,et al.  Formulation and treatment of frictional contact problems using finite elements , 1992 .

[2]  L. Anand,et al.  An internal variable constitutive model for hot working of metals , 1989 .

[3]  Tomaž Rodič,et al.  Shape sensitivity analysis of large deformation frictional contact problems , 2002 .

[4]  T. Laursen.  Computational Contact and Impact Mechanics: Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis , 2002 .

[5]  Byung-Min Kim,et al.  Application of artificial neural network and Taguchi method to preform design in metal forming considering workability , 1999 .

[6]  J. C. Simo,et al.  An augmented lagrangian treatment of contact problems involving friction , 1992 .

[7]  Nicholas Zabaras,et al.  An object-oriented programming approach to the Lagrangian FEM analysis of large inelastic deformations and metal-forming processes , 1999 .

[8]  Peter Wriggers,et al.  Nonlinear Computational Mechanics: State of the Art , 1991 .

[9]  Luísa Costa Sousa,et al.  Inverse methods in design of industrial forging processes , 2002 .

[10]  N. Zabaras,et al.  Design across length scales: a reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties , 2004 .

[11]  N. Zabaras,et al.  A continuum sensitivity method for the design of multi-stage metal forming processes , 2003 .

[12]  Jean-Loup Chenot,et al.  Inverse methods applied to metal forming processes , 2000 .

[13]  S. M. Hwang,et al.  Application of a genetic algorithm to the optimal design of the die shape in extrusion , 1997 .

[14]  P. Hajela,et al.  COMPUTATIONAL MECHANICS FOR THE TWENTY- FIRST CENTURY , 2007 .

[15]  Nicholas Zabaras,et al.  An updated Lagrangian finite element sensitivity analysis of large deformations using quadrilateral elements , 2001 .

[16]  Jean-Loup Chenot,et al.  Inverse problems in finite element simulation of metal forming processes , 1996 .

[17]  Nicholas Zabaras,et al.  A proper orthogonal decomposition approach to microstructure model reduction in Rodrigues space with applications to optimal control of microstructure-sensitive properties , 2003 .

[18]  Nicholas Zabaras,et al.  Deformation process design for control of microstructure in the presence of dynamic recrystallization and grain growth mechanisms , 2004 .

[19]  Nicholas Zabaras,et al.  Computational design of deformation processes for materials with ductile damage , 2003 .

[20]  Nicholas Zabaras,et al.  A continuum sensitivity method for finite thermo‐inelastic deformations with applications to the design of hot forming processes , 2002 .

[21]  Nicholas Zabaras,et al.  Shape optimization and preform design in metal forming processes , 2000 .