Drucker stability

Drucker's first stability criterion (first proposed by Rodney Hill and also called '''Hill's stability criterion''') is a strong condition on the incremental internal energy of a material which states that the incremental internal energy can only increase. The criterion may be written as follows: : \text{d}\boldsymbol{\sigma}:\text{d}\boldsymbol{\varepsilon} \ge 0 , where dσ is the stress increment tensor associated with the strain increment tensor dε through the constitutive relation. == Drucker's stability postulate ==

Drucker's postulate is applicable to elastic-plastic materials and states that in a cycle of plastic deformation the second degree plastic work is always positive. This postulate can be expressed in incremental form as : \text{d}\boldsymbol{\sigma}:\text{d}\boldsymbol{\varepsilon}_p \ge 0 , where dεp is the incremental plastic strain tensor. ==References==