Finite viscoelasticity model accounting for bond stretch in elastomers

Fracture in elastomers occurs when the internal energy reaches the critical value, as is well posited in the Lake-Thomas theory. Hence, constitutive theories of elastomers have been recently developed further to incorporate the "bond stretch", by which the stretching of molecular bonds (or effective Kuhn segments) is described. In this work, we present a constitutive theory for finite viscoelasticity that involves the bond stretch in elastomers. Existing bond stretch models can physically demonstrate the fracture processes in elastomeric networks, but the bond stretch associated with rate-dependent deformation has not been taken into account. We extend the bond stretch model to account for the viscoelastic responses based on reptation of elastomeric chains. The reptation leads to the rate-dependent evolution of the internal energy of an elastomeric network, by which the rate-dependent stress responses are simply captured within the new bond stretch model. Our constitutive theory is capable of describing the key viscoelastic features including rate-dependent stiffness, relaxation, and creep without handling any complex finite deformation kinematics; rather, the microscopic forces are taken into account within a simple rheological setting. Our model can also be further extended to account for the rate-dependent fracture widely found in elastomers.