Functionals of the direct and inverse extreme quasistatic problems of forming structural components are considered. The uniqueness and stability of the solution to such a problem is proved for various boundary conditions of inelastic deformation when the sufficient uniqueness conditions are satisfied for the corresponding boundary value problems. The constructed functionals are used to solve the inverse problems numerically with consideration of the formulation of direct problems of inelastic deformation and elastic unloading. The springback is determined by solving the direct forming problem with a finite element method and is used in an iterative method for solving the inverse problem. A number of modifications for this iterative method are proposed depending on the choice of coefficients and regularizing functionals. The developed methods are realized in the MSC.Marc system. The software tools of this system intended for the introduction of new creep models are used to solve the inverse forming problems with consideration of properties of modern aluminum alloys.

Keywords: inverse forming problems, variational inequalities, uniqueness, stability, iterative regularization methods, finite element method.

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