Branching of strain histories for nonlinear viscoelastic solids with a strain clock

An important class of constitutive equations for nonlinear viscoelastic response utilizes the concept of a strain clock. The clock takes the form of a material time variable which is defined in terms of the strain history and which increases faster than physical time. Important consequences of the strain clock are that stress relaxation and creep occur faster as strain increases, and the stress may not increase monotonically with time. In this work, we discuss whether this non-monotonic response implies that strain histories may branch into multiple histories.