Method for Determining a Polynomial Constitutive Equation with Temperature and Strain-Rate Dependence by the AIC

A method for determining a strain-rate and temperature dependent dynamic constitutive equation is described. The constitutive equation is determined as a polynomial by approximating measured data without detail considerations based on the underlying material science. Generally a polynomial approximates given data more precisely as the degree is increased. However, as the degree increases, the calculation becomes more difficult. The method we describe here not only derives the unknown coefficients in the polynomial but also reveal the optimum degree by the evaluation of an information criterion. We apply the method to the example of a temperature and strain-rate dependent dynamic constitutive equation for steel SS400. The derived dynamic constitutive equation convincingly modeled elasto-plastic deformation of steel SS400 under a wide range temperatures and strain rates. (AIC: Akaike Information Criterion.)