A novel evolutionary algorithm for determining unified creep damage constitutive equations

Abstract

The determination of material constants within uniÿed creep damage constitutive equations from experimental data can be formulated as a problem of ÿnding the global minimum of a well deÿned objective function. However, such an objective function is usually complex, non-convex and non-di erentiable. It is di cult to be optimised by classical gradient-based methods. In this paper, the di culties in the optimisation are ÿrstly identiÿed. Two di erent objective functions are proposed, analysed and compared. Then three evolutionary programming algorithms are introduced to solve the global optimisation problem. The evolutionary algorithms are particularly good at dealing with problems which are complex, multi-modal and non-di erentiable. The results of the study shows that the evolutionary algorithms are ideally suited to the problem. Computational results of using the algorithms to determine the material constants in a set of physically based creep damage constitutive equations from experimental data for an aluminium alloy are presented in the paper to show the e ectiveness and e ciency of the three evolutionary algorithms.?

Unified constitutive modelling for two-phase lamellar titanium alloys at hot forming conditions

“…Evolutionary programming optimisation techniques, minimizing the residuals between the computed target values and experimental data, have been usually used to determine the model parameters [35]. The details of the optimisation method and the corresponding numerical procedure for this type of problem are described by Li et al [36], Lin et al [37,38], Cao et al [39,40] and Zhou et al [41]. Referring to the objective function developed by Cao and Lin [39], two sub-objective functions were defined as:…”

Experimental and Numerical Studies on the Formability of Materials in Hot Stamping and Cold Die Quenching Processes

“…USIBOR 1500P boron steel and AA6082 has been used throughout this research. The constants in the equations are determined by the fitting of their corresponding experimental data using optimization methods detailed by Li et al 10 . Figure 2 and Figure 3 show the comparison between computed (solid curves) and experimental (symbols) stress-strain relationships for boron steel and Aluminum alloy, respectively, and close agreement has been obtained for both cases.…”

A novel criterion for determination of material model parameters

“…Recently, the mentioned criteria were satisfied by Lin et al [1,2,3] with the introduction of new objective functions formulations and automatic weighting factors. Similar to the true strain definition, the concept of true (logarithm) error definition was also used in order to increase the function sensitivity to the parameters.…”

“…This tries to ensure that all the experimental and computed data are involved in the optimisation and the predicted data will be pushed towards the corresponding experimental data. The objective function formulation suggested by Lin and coworkers [1,2] is…”