Kinematic extremum theorems for holonomic plasticity (Q918777)

The paper deals with elasto-plastic constitutive relations in finite terms in the framework of deformation or holonomic theories. The elasto- plastic behaviour is governed by Hooke's relation between the stress and the elastic part of strain, supposing the additive decomposition of strain tensor into elastic and plastic components. The yield functions depend on stress and possibly on plastic strains and/or on plastic multipliers, which can be expressed as a function of plastic strains, in contrast to rate plasticity. The additional assumptions allow to obtain a static inequality (which is a holonomic version of Drucker's stability postulate) and a kinematic inequality. Two extremum theorems are proved, one characterizing the material response to given strains and the second the structural response to given loads. The evaluation of material response is reduced to solve a nonlinear programming problem. Two examples illustrate meanings of the relations derived in the proposed holonomic model.