  We propose a theoretical framework for dealing with a transient polymer
network undergoing small deformations, based on the rate of breaking and
re-forming of network crosslinks and the evolving elastic reference state. In
this framework, the characteristics of the deformed transient network at
microscopic and macroscopic scales are naturally unified. Microscopically, the
breakage rate of the crosslinks is affected by the local force acting on the
chain. Macroscopically, we use the classical continuum model for rubber
elasticity to describe the structure of the deformation energy, whose reference
state is defined dynamically according to when crosslinks are broken and
formed. With this, the constitutive relation can be obtained. We study three
applications of the theory in uniaxial stretching geometry: for the stress
relaxation after an instantaneous step strain is imposed, for the stress
overshoot and subsequent decay in the plastic regime when a strain ramp is
applied, and for the cycle of stretching and release. We compare the model
predictions with experimental data on stress relaxation and stress overshoot in
physically bonded thermoplastic elastomers and in vitrimer networks.
