A model of cutting cellular elastic materials

A plane model for the cutting of cellular elastic material by a rigid triangular non-slender cutter is developed. The cutter propagates quasi-statically with Coulomb friction at the boundaries causing rupture of the cells in front of the vertex and densification of the material along the cutter's faces. Postulating a wedge-shaped form for the compacted material allows formulating a mixed boundary value problem which is solved exactly by means of Cauchy type integrals. Fracture criteria for rupture and densification processes are applied to adjust the formal solution and to find the cutting regime parameters. The wedging phenomenon with a leading crack and the bearing strain process with a built-up edge are predicted for the cases when cutting is impossible. Numerical examples with graphical illustrations are presented.