There has been considerable effort to describe the non-linear viscoelastic response of glassy materials by using constitutive equations in which the material time or clock is affected by stress induced changes in the 'free volume' or glassy structure of the material. Experiments have been performed using the NIST torsional dilatometer in order to simultaneously measure the volume (structure) and viscoelastic response of samples subjected to carefully controlled thermomechanical histories. Temperature-jump experiments were performed in which equilibrated samples are rapidly up or down quenched and subjected to intermittent torsional deformations to follow the evolution of the viscoelastic response of the glass simultaneous with the volume recovery. It is found that, even when the magnitude of the applied torsional deformations is well into the non-linear range, but below yield, the volume recovery response from the quench is unaffected. This result is interpreted to imply that the structure of the glass is decoupled from the applied stress field. The significance of this for the development of constitutive equations governing the viscoelastic response of glasses is discussed. Additional results showing that the aging response and volumetric response occur on different timescales are discussed.