Energy release rate of small cracks in hyperelastic materials

This is the preprint of an article that will appear in the International Journal of Non-linear Mechanics

Energy release rate of small cracks in hyperelastic materials by M. Ait-Bachir, W. V. Mars, and E. Verron

Abstract. The energy release rate of a small crack in an infinite hyperelastic medium, and subjected to large strain multiaxial loading conditions, is derived by considering the balance of configurational stresses acting on two planes: one cutting the center of the crack face, and the other at an infinite distance in front of the crack tip. The analysis establishes that the energy release rate of a small crack is always proportional to the size of the crack, irrespective of the loading conditions and the crack orientation. The balance of configurational stresses is illustrated for several benchmark cases including simple extension, pure shear and equibiaxial extension, and for perpendicular and inclined cracks.