A Phase‐Field Fracture Model of Nearly Incompressible Hyperelastic Material Based on a Mixed Formulation

Source abstract

ABSTRACT Hyperelastic materials play a crucial role in modern applications due to their unique properties, especially their flexibility, stretchability, and resilience. However, the incompressibility constraint is an unavoidable challenge in the modeling of most hyperelastic materials, and makes it even more challenging to successfully explain or reproduce crack propagation via numerical simulations. Mixed formulations, for example, the so‐called Q1P0 approach, are commonly used to avert locking issues due to incompressibility at finite deformations. In the present study, the Q1P0 approach is derived based on the Hu–Washizu three‐field variational principle, yielding a single‐field displacement–based formulation. Afterwards, the phase‐field approach is incorporated to predict finite strain fracture of nearly incompressible hyperelastic materials. With a consistently derived and condensed description, the multifield formulation is reduced into a standard displacement–phase‐field approach. A special phase‐field degradation function is particularly incorporated into the volumetric contribution to release the pressure term faster and, consequently, to allow crack opening, which mediates the innate contradiction between incompressibility constraint and diffuse crack opening. Subsequently, several numerical examples are presented to illustrate the characteristics of the proposed formulation.