Estimation of the dynamic constitutive equations by using the method of nonlinear least squares

An estimation method of the dynamic constitutive equations using the method of least squares is described. In this paper, the unknown parameters in the constitutive equations of which tthe functional form is known were estimated. The estimation is performed by using the method of nonlinear least squares utilizing the Gauss-Newton method because the constitutive equations are nonlinear. Numerical simulation were done such that the unknown parameters in the constitutive equation were estimated from the value of the strain wave in a long bar subjected to longitudinal impact. The stability of the estimation and influence of experimental error on the estimated parameters were examined. As a result, it was concluded that the present method is practically useful.