An implicit unitless error and step-size control method in integrating unified viscoplastic/creep ODE-type constitutive equations

A series of numerical analyses are carried out to investigate the difficulties in numerical integration of unified viscoplastic/creep constitutive equations, which are normally represented as a system of ordinary differential equations (ODEs). The problems of numerically integrating the constitutive equations are identified and analysed. To overcome the stiffness problems, implicit methods are used for the numerical integration and a generic technique is introduced to calculate the Jacobian matrix. A normalization technique is introduced in the paper to convert the integration errors for each time increment to unitless effors. Thus, a single tolerance can be used to control the accuracy and step size in integrating a set of unified viscoplastic/ creep constitutive equations. In addition, an implicit step-size control method is proposed and used in the integrations. This method reduces the possibifity of rejection of an integration increment due to poor accuracy.