Abstract: In this paper, the deformation theory in plasticity is formulated in the variational inequality, which can relax the constraint conditions of the constitutive equations. The new form makes the calculation more convenient than general energy forms and have reliable mathematical basis. Thus the plasticity theory may be solved by means of the quadratic programming instead of the iterative methods. And the solutions can be made in one step without any diversion of the load.

Key words: deformation theory in plasticity, variational inequality, quadratic programming