Interconversion between Relaxation Modulus and Creep Compliance for Viscoelastic Solids

Abstract

Methods of interconversion between relaxation modulus and creep compliance for linear viscoelastic materials are discussed and illustrated using data from asphalt concrete. Existing methods of approximate interconversion are reviewed and compared for their approximating schemes. A new approximate interconversion scheme that uses the local log-log slope of the source function is introduced. The new scheme is based on the concept of equivalent time determined by rescaling the physical time. The rescaling factor, which can be interpreted as a shift factor on a logarithmic time axis, is dictated by the local slope of the source function on log-log scales. The unknown target function at a given time is obtained by taking the reciprocal of the source function evaluated at an equivalent time. Although the method is developed using a mathematical relationship based on the power-law representations of relaxation modulus and creep compliance, the method is not limited to material functions characterized by power-laws but can be applied to general, non-power-law material functions as long as the relevant material behaviors are broadband and smooth on logarithmic scales. The new method renders good results especially when the log-log slope of the source function varies smoothly with logarithmic time.