The dynamic mechanical behavior of a polyurethane used as an interlayer in a laminated windshield construction is studied by dynamic mechanical analysis, compression testing at various strain rates (0.001/s to 7000/s), and various temperatures (-40 degrees C to 25 degrees C) by using the universal testing machine and split Hopkinson pressure bar (SHPB) equipped with temperature controllers. The obtained results show that the mechanical behavior of the polyurethane interlayer is sensitive to temperature and strain rate. Under dynamic loading condition, stress-strain curves at -40 degrees C exhibit the transition from rubbery to glassy. On the basis of the constitutive theory and the experimental data, a one-dimension thermal-hyper-viscoelastic constitutive equation is proposed to describe the large compressive deformation response of the polyurethane interlayer over wide ranges of strain rates and temperatures. The parameter A(30) of the function phi(I-1,I-2) is significant to describe the trend of the stress-strain curve at larger strain. The stress-strain curves at low strain rate and low temperature can overlap the stress-strain curves at higher strain rate and higher temperature; there may be an equivalent relationship between temperature and strain rate. POLYM. ENG. SCI., 55:1864-1872, 2015. (C) 2014 Society of Plastics Engineers