A study on formulation of objective functions for determining material models

Optimisation techniques have been developed and used to determine material constants arising in unified creep/viscoplastic constitutive equations based on experimental data. Objective functions (OF) have been formulated as pointers to the quality of fit between the equations and experimental data and a set of criteria is presented to assess the suitability of the objective functions. Convergence features of two existing objective functions are analysed. The problems of using these objective functions are studied. To overcome difficulties arising in the existence of different scales of individual sub-objectives, a novel error definition is introduced, which has a natural unitless form and can provide a measure for “true” error. A novel weighting technique is introduced, which can also be chosen automatically to compensate the loss of credits in individual data points and curves. Using these techniques, a novel objective function is formulated, which meets the set criteria. The objective function, together with an evolutionary programming (EP) solver, are employed to determine material constants in three sets of unified constitutive equations which are formulated to match experimental data. The convergent features of the objective functions are compared and analysed.