Determination Method for Dynamic Constitutive Equations Based on an Information Criterion.

Abstract

This paper presents an easy determination method for the dynamic constitutive equations of materials with strain-rate sensitivity. The proposed method will easily determine a simple constitutive equation from the results of ordinary impact tests. Previously, the determination of dynamic constitutive equations is usually attempted from a metallographical or physical standpoint. Such attempts often need detailed consideration, and most of the derived equations become complex. Furthermore, the estimation of the involved unknown parameters in the equations is also difficult. If simple dynamic constitutive equations can be determined without especially physical considerations, the simulation for mechanical deformations caused by impact will become easy. Thus, this paper tries to determine dynamic constitutive equations as polynomials which can describe various curves and be easily treated. Polynomials approximate given data more precisely with increase in the number of the involved parameters. However, as the number of parameters increases, the calculation of the equations become more difficult. Furthermore, it is not necessarily appropriate that the equation fits measured data considerably precisely, because the measured data usually contain some errors. Therefore this paper proposes the determination method for dynamic constitutive equations based on an information criterion 'AIC'. The information criterion will evaluate the appropriateness of approximate equations and reveal the required minimum number of the parameters to be used. The proposed method demonstrates that 'AIC' will easily determine appropriate dynamic constitutive equations.