Fracture of viscoelastic solids modeled with a modified phase field method

Fracture of viscoelastic solids plays an important role in many applications but it is not yet well understood. In addition to the time and rate dependent response of viscoelastic materials, fracture of these solids is governed by nonlinear processes at the fracture process zone and could also be accelerated by viscous energy dissipation. To this end, we propose a new phase field formulation in which fracture of viscoelastic solids is driven by both elastic and viscous components of the energy. The formulation requires a single additional parameter to quantify the portion of the viscous energy that contributes to fracture and is shown to be thermodynamically consistent. Viscoelastic material behavior, in the form of a Generalized Maxwell model, is obtained through a standard Prony-series type expansion. Fracture driven by viscous dissipation is studied on several important benchmark problems, including (i) a bar under creep, relaxation, strain rate and cyclic loadings, and (ii) two 3-point asphalt-beam bending problems that lead to crack propagation under mode I and mixed mode conditions. It is shown that at low strain rates viscous dissipation accelerates the fracture growth rate but essentially does not affect the crack path, while at high rates the effect of viscous dissipation is minor.