Failing softly: a fracture theory of

highly-deformable materials

 

T. Goldman Boue´,a R. Harpaz,b J. Fineberga and E. Bouchbinder*b

 

Highly-deformable materials, from synthetic hydrogels to biological tissues, are becoming increasingly

important from both fundamental and practical perspectives. Their mechanical behaviors, in particular the

dynamics of crack propagation during failure, are not yet fully understood. Here we propose a theoretical

framework for the dynamic fracture of highly-deformable materials, in which the effects of a dynamic crack

are treated with respect to the nonlinearly deformed (pre-stressed/strained), non-cracked, state of the

material. Within this framework, we derive analytical and semi-analytical solutions for the near-tip

deformation fields and energy release rates of dynamic cracks propagating in incompressible neo-Hookean

solids under biaxial and uniaxial loading. We show that moderately large pre-stressing has a marked

effect on the stress fields surrounding a crack’s tip. We verify these predictions by performing extensive

experiments on the fracture of soft brittle elastomers over a range of loading levels and propagation

velocities, showing that the newly developed framework offers significantly better approximations to the

measurements than standard approaches at moderately large levels of external loadings and high

propagation velocities. This framework should be relevant to the failure analysis of soft and tough, yet

brittle, materials.