r7.01.39 Rankine’s law

Summary:

This document introduces the method for resolving Rankine’s law.

• 1. Introduction
• 2. Local integration of Rankine’s law
  • 2.1. Cases where only one mechanism is active
  • 2.2. Cases where two mechanisms are active
  • 2.3. Case of the projection at the top of the cone
  • 2.4. Internal variables of the model
• 3. Expression of the tangent matrix in the main base
  • 3.1. Cases where only one mechanism is active
  • 3.2. Cases where two mechanisms are active
  • 3.3. Case of the projection at the top of the cone
• 4. Expression of the tangent matrix in the global base
  • 4.1. Introductory remark
  • 4.2. Application to the case of Rankine
  • 4.3. Scheme for resolving the law of behavior
• 5. Appendix: some results on isotropic symmetric tensors of order two
  • 5.1. Definition of an isotropic symmetric tensor
  • 5.2. Derivative of an isotropic tensor function of order two
• 6. Appendix: tensor ratings convention