Colonnetti's minimum principle extension to generally non-linear materials

In this paper two minimum principles are presented for the continuum problem with general non-linear materials (holonomic, non-holonomic, with hardening or softening, time-dependent, etc.). The proof of the first principle is based on the use of an elastic auxiliary problem associated to the original non-linear one and on the interpretation of the actual inelastic strains as unknown strains imposed on the elastic auxiliary solid. In a dual way the proof of the second principle is given through the imposition of suitable stresses on the elastic auxiliary solid. Classical principles of elasticity and incremental elastoplasticity are then derived from the new principles as particular cases. Three simple illustrative examples are given.