  Polyborosiloxane (PBS) is an important rate-stiffening soft polymer with
dynamic, reversible crosslinks used in applications ranging from self-healing
sensing and actuation to body and structural protection. Its highly
rate-dependent response, especially for impact-mitigating structures, is
important. However, the large strain response of PBS has not been characterized
over quasi-static to high strain rates. Currently, there are no constitutive
models that can predict the strongly rate-dependent large-deformation
elastic-viscoplastic response of PBS. To address this gap, we have developed a
microstructural physics motivated constitutive model for PBS and similar soft
polymers and polymer gels with dynamic crosslinks to predict their large
strain, non-linear loading-unloading, and significantly rate-dependent
response. We have conducted compression experiments on PBS up to true strains
of $\sim$125$\%$ over a wide strain rate range of 10$^{-3}$ s$^{-1}$ to
10$^{3}$ s$^{-1}$. The model reasonably accurately captures the response of PBS
over six decades of strain rates. We propose boron-oxygen coordinate-bond
dynamic crosslinks with macroscopic relaxation timescale $\tau \approx 3$ s and
temporary entanglement lockups at high strain rates acting as crosslinks with
$\tau \approx 0.0005$ s as the two types of crosslink mechanisms in PBS. We
have outlined a numerical update procedure to evaluate the convolution-like
time integrals arising from dynamic crosslink kinetics. Experiments involving
three-dimensional inhomogeneous deformations were used to verify the predictive
capabilities of our model and its finite element implementation. The modeling
framework can be adopted for other dynamically crosslinked rate-stiffening soft
polymers and polymer gels that are microstructurally similar to PBS.
