Least Square Optimization Techniques Applied on Sheet Metal Forming - Inverse Identification of Constitutive Parameters and Optimizatin of Process Parameters

The major subject of the thesis is nonlinear least square optimisation techniques, identification of constitutive parameters through inverse modeling and process/product optimization. The application area is sheet metal forming. The sheet metal forming domain is highly matured with respect to quality and stability of simulation software and constitutive models. Numerical simulation of the sheet metal forming process is widely used in industry where the automotive industry is one of the driving forces. The optimization techniques described and utilized in the thesis are based on the second-order Taylor approximation of a continuous object function, where the object function is defined as a sum of squares or a set of equations, i.e. the object function is iteratively minimized, and during iterations the step size is controlled by a trust region scheme. Totally structured secant methods are utilized for approximation of the second order term of the Hessian matrix. The research in this thesis considers inverse modeling where the constitutive parameters are identified directly from a deep drawing operation by minimizing the least square error between empirical data and the data produced by a coherent finite element model. The main conclusion is that all constitutive parameters should be subject to identification including friction coefficients. The second research topic is optimization of process/product parameters, a few examples are given, e.g. geometric optimization of flexible aluminum tubes, tube hydro forming (geometric fit), two step hydro mechanical forming where the subject is tool geometry/layout and geometric fit. Nonlinear least square techniques and trust region methods are applied for solving the optimization problems. The thesis was defended in June 2003. Supervisor: Karl Brian Nielsen. (Benny Endelt, Department of Production, AAU)