Thermodynamic functions for ageing viscoelasticity: integral form without internal variables

Viscoelastic materials whose creep and relaxation functions depend on the age at loading are considered[ First the material is assumed to follow the solidi_cation theory\ which explains ageing of concrete by gradual deposition of layers of newly solidi_ed non!ageing viscoelastic constituent "cement gel# on the pore walls[ It is shown that the well!known classical Staverman and Schwarzl|s and Mandel|s formulae for the densities of Helmholtz free energy\ free enthalpy and dissipation in a non!ageing viscoelastic material can be gen! eralized to the case of ageing by double Stieltjes integrals over the strain or stress histories[ Their integrands contain only the relaxation or compliance functions and their rates\ but not the internal variables nor the properties of constituents[ The expressions obtained for the free energy and free enthalpy are subsequently shown to possess in general "without restriction to the solidi_cation theory# the property of a potential for the stress or strain\ respectively[ Consequently\ if one formulates three!dimensional expressions for the free energy or free enthalpy on the basis of the solidi_cation theory\ one may\ conversely\ obtain constitutive equations for ageing viscoelasticity that are consistent with continuum thermodynamics[ An expression for the dissipated power of an ageing material is also derived[ The results should prove useful for approximate solutions\ bounds on structural response\ and numerical solution algorithms