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A continuum sensitivity method for finite thermo-inelastic deformations with applications to the design of hot forming processes. (English) Zbl 1026.74022

Summary: A computational framework is presented to evaluate the shape as well as non-shape (parameter) sensitivity of finite thermo-inelastic deformations using the continuum sensitivity method (CSM). Weak sensitivity equations are developed for large thermo-mechanical deformations of hyperelastic thermo-viscoplastic materials that are consistent with the kinematic, constitutive, contact and thermal analyses used in the solution of the direct deformation problem. The sensitivities are defined in a rigorous sense, and the sensitivity analysis is performed in an infinite-dimensional continuum framework. The effects of perturbation in the preform, die surface, or other process parameters are carefully considered in the CSM development for the computation of the die temperature sensitivity fields. The direct deformation and sensitivity deformation problems are solved using the finite element method. The results of the continuum sensitivity analysis are validated extensively by a comparison with those obtained by finite difference approximations (i.e. using the solution of a deformation problem with perturbed design variables). The effectiveness of the method is demonstrated with a number of applications in the design optimization of metal forming processes.

MSC:

74F05 Thermal effects in solid mechanics
74C20 Large-strain, rate-dependent theories of plasticity
74S05 Finite element methods applied to problems in solid mechanics
74P10 Optimization of other properties in solid mechanics

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References:

[1] Parameter Sensitivity in Non-Linear Mechanics?Theory and Finite Element Computations. Wiley: New York, 1997.
[2] Badrinarayanan, Computer Methods in Applied Mechanics and Engineering 129 pp 319– (1996)
[3] Zabaras, International Journal for Numerical Methods in Engineering 48 pp 679– (2000)
[4] A continuum sensitivity analysis of large deformations with applications to metal forming process design. Ph.D. Dissertation, Cornell University: Ithaca, NY, 2001.
[5] Srikanth, Computer Methods in Applied Mechanics and Engineering 190 pp 1859– (2000)
[6] Srikanth, International Journal for Numerical Methods in Engineering 52 pp 1131– (2001)
[7] Chenot, International Journal for Numerical Methods in Engineering 39 pp 51– (1996)
[8] Chenot, International Journal for Numerical Methods in Engineering 39 pp 33– (1996)
[9] Balagangadhar, International Journal for Numerical Methods in Engineering 49 pp 933– (2000)
[10] Ant?nez, Computer Methods in Applied Mechanics and Engineering 161 pp 113– (1998)
[11] Zhao, International Journal for Numerical Methods in Engineering 40 pp 1213– (1997)
[12] Gao, International Journal for Numerical Methods in Engineering 45 pp 1349– (1998)
[13] Doltsinis, International Journal for Numerical Methods in Engineering 45 pp 661– (1999)
[14] Chung, International Journal for Numerical Methods in Engineering 42 pp 1343– (1998)
[15] Michaleris, International Journal for Numerical Methods in Engineering 47 pp 1807– (2000)
[16] Fernandes, Journal of Materials Processing Technology 87 pp 247– (1999)
[17] Rodrigues, International Journal for Numerical Methods in Engineering 42 pp 631– (1998)
[18] Kobayashi, International Journal of Mechanical Sciences 22 pp 699– (1980)
[19] Kobayashi, International Journal of Mechanical Sciences 22 pp 707– (1980)
[20] Chenot, Engineering Computations 12 pp 687– (1995)
[21] Anand, International Journal of Plasticity 1 pp 213– (1985)
[22] Srikanth, International Journal for Numerical Methods in Engineering 45 pp 1569– (1999)
[23] On the formulation and numerical treatment of finite deformation frictional contact problems. In Nonlinear Computational Mechanics?State of the Art, (eds). Springer Verlag: Berlin, 1991; 716-736.
[24] Srikanth, Engineering with Computers 15 pp 37– (1999)
[25] Zabaras, International Journal of Mechanical Sciences (2001)
[26] Weber, Computer Methods in Applied Mechanics and Engineering 79 pp 173– (1990)
[27] Brown, International Journal of Plasticity 5 pp 95– (1989)
[28] Processes and Materials of Manufacturing. Prentice-Hall: New York, 1998.
[29] Computational Partial Differential Equations: Numerical Methods and Diffpack Programming. Springer: New York, 1999. · Zbl 0929.65098
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