Toupin-Type Decay and Saint-Venant’s Principle

Abstract

Toupin’s Theorem plays the most influential role in the history of development concerning Saint-Venant’s Principle. We now review the history and the previous works, distinguishing Saint-Venant type decay from Toupin-type decay and arguing that Toupin’s Theorem is not a formulation of Saint-Venant’s Principle; Saint-Venant’s Principle stated by Love can be disproved mathematically from Toupin’s Theorem, so Toupin’s Theorem is mathematically inconsistent with Saint-Venant’s Principle; Modified Saint-Venant’s Principle can be proved or formulated, though Saint-Venant’s Principle in its general form stated by Boussinesq and Love is not true.