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The time‐dependent behavior of linearly viscoelastic materials is known to be very sensitive to changes in temperature and in solvent (water) concentration. Following an investigation by the authors of this sensitivity in terms of the associated small volume changes, a nonlinearly viscoelastic model of constitutive behavior was formulated earlier in terms of the free volume concept and evaluated in terms of experiments on poly(vinyl acetate). Following a brief presentation of the earlier results these concepts are expanded and refined in the present paper to deal with transient deformation histories under pressure. In this connection, model computations explore the effect of simultaneous pressurization and straining. In addition the effect of “ageing” the polymer under pressures of various magnitudes and for different lengths of time are investigated. It becomes clear that the yield phenomenon depends sensitively on pressure and on the ageing time. In addition, the volume change under transient thermal histories in the glass transition range is explored, largely in terms of Kovacs' experimental data and attendant computations. These considerations are presented from a unified point of view of nonlinear thermoviscoelastic constitutive behavior, principally with phenomenological material description in mind. These computations provide guidance to the design of experiments for the proper determination of the relevant material functions and seem to indicate a need for the reevaluation of certain experimental procedures in the time histories of thermal material characterization.

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