1. Mechanical modeling

1.1 Assumptions and nature of the problems to be solved

The simplest models of chip formation are purely mechanical, i.e. they neglect thermal effects. The mechanical behavior considered is generally inelastic (elastic deformation neglected), with plasticity without strain-hardening. This material, known as rigid perfectly plastic or RPP, is therefore characterized by the maximum permissible shear stress k . The Young's modulus of an RPP body is therefore assumed to be infinite, i.e. in practice very large compared to k, the maximum permissible shear stress: E/k >> 1.

Recall that, for a material verifying the von Mises plasticity criterion and the associated plastic flow law, $k={\sigma }_0\text{/}\sqrt{3}$...