Steady-State Crack Propagation in Rubber-Like Materials: from Neo-Hookean to Gent-Type Models

We investigate steady-state mode I crack propagation in nonlinear elastic solids using the finite element method. The neo-Hookean model yields a parabolic crack opening profile and r−1/2 strain singularity, where r is the distance ahead of the crack tip, for all crack velocities considered, consistent with linear elastic fracture mechanics despite its nonlinearity. In contrast, Gent-type models exhibit sharper crack opening profiles and strain plateaus near the crack tip. These findings differ from the weakly nonlinear theory, which predicts a sharp, non-parabolic crack profile and r−1 singularity. Compared to the neo-Hookean case, Gent-type models show weaker stress, strain, and their singularities for the same crack velocity and applied strain, implying that strong nonlinearity may improve toughness.