Constitutive equations for thermomechanical deformations of glassy polymers

Poly-Carbonate (PC) and Poly-Methyl-Methacrylate (PMMA) are lightweight and mechanically tough transparent glassy polymers. Their mechanical behavior at low to moderate strain rates has been well characterized; however, that at high strain rates needs additional work. We propose two modifications to existing pressure-dependent viscoplastic constitutive equations that enable one to simulate better mechanical deformations of PC and PMMA at high strain rates. First, the elastic moduli are taken to depend upon the current temperature and the current effective strain rate. Second, two internal variables are introduced to better characterize the strain softening of the material at high strain rates. A technique to find values of newly introduced material parameters is described. We compute the local temperature rise due to energy dissipated during plastic deformations. The true axial stress vs. the true axial strain curves in uniaxial compression from numerical simulations of the test configurations at high strain rates using the proposed constitutive equations are found to agree well with the experimental results available in the literature.