Parameter identification of superplastic constitutive model by GA-based global optimization method

Abstract The successful application of superplastic constitutive model considering grain growth depends on how well the material parameters are identified. However, it is difficult to obtain satisfactory parameters by using the traditional parameter identification method. The reasons are due to that it is difficult to separate one physical process from other physical processes involved in the model. In this paper, the material parameters are identified by inverse analysis. The objective function is first provided, and then a hybrid optimization method has been developed and used to identify the parameters. The developed optimization method incorporates the strengths of GA, the Levenberg–Marquardt algorithm and the augmented Gauss–Newton algorithm. The difficulty of choosing appropriate initial values for the parameters in the traditional optimization technique is overcome by applying the GA and the shortcoming of the slow convergent speed of the GA is surmounted by applying the Levenberg–Marquardt algorithm and the augmented Gauss–Newton algorithm. At last, taking Ti–6Al–4V as an example, a set of satisfactory material parameters is obtained. The calculated results agree with the experimental results well.

[1]  Francisco Herrera,et al.  Tackling Real-Coded Genetic Algorithms: Operators and Tools for Behavioural Analysis , 1998, Artificial Intelligence Review.

[2]  Amit K. Ghosh,et al.  Mechanical behavior and hardening characteristics of a superplastic Ti-6AI-4V alloy , 1979 .

[3]  Jorge J. Moré,et al.  The Levenberg-Marquardt algo-rithm: Implementation and theory , 1977 .

[4]  Jean-Claude Gelin,et al.  An inverse solution procedure for material parameters identification in large plastic deformations , 1996 .

[5]  P. Preux,et al.  Towards hybrid evolutionary algorithms , 1999 .

[6]  S. Sorooshian,et al.  Effective and efficient global optimization for conceptual rainfall‐runoff models , 1992 .

[7]  J. Betts.  Solving the nonlinear least square problem: Application of a general method , 1976 .

[8]  John E. Dennis,et al.  An Adaptive Nonlinear Least-Squares Algorithm , 1977, TOMS.

[9]  Rolf Mahnken,et al.  Parameter identification for viscoplastic models based on analytical derivatives of a least-squares functional and stability investigations , 1996 .

[10]  Otto T. Bruhns,et al.  On the simultaneous estimation of model parameters used in constitutive laws for inelastic material behaviour , 1998 .

[11]  Jianguo Lin,et al.  GA-based multiple objective optimisation for determining viscoplastic constitutive equations for superplastic alloys , 1999 .

[12]  D. Bertsekas.  Projected Newton methods for optimization problems with simple constraints , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[13]  Ya-Xiang Yuan,et al.  Optimization theory and methods , 2006 .

[14]  Tzung-Pei Hong,et al.  Simultaneously Applying Multiple Mutation Operators in Genetic Algorithms , 2000, J. Heuristics.

[15]  D. Schnur,et al.  An inverse method for determining elastic material properties and a material interface , 1992 .

[16]  A. Mukherjee,et al.  A model for the rate-controlling mechanism in superplasticity , 1980 .