The control of damage using optimization methods is considered supplementary to material and structural analysis. During all three funding periods and with increasing complexity, the forming process and the wrought product are to be constructed such that lifetime is maximized while damage is controlled. These aims should be achieved by modeling and solving different mathematical optimization problems (objective function, constraints, design variables). Academic and industrial optimization strategies differ significantly in the effort made for analytical preparation of the optimization problem, in the choice of algorithms, and, hence, the cost of the numerical calculation. The academic (based on mechanical principles) as well as the industrial perspective (based on the industrial forming process) should be analyzed and joined in the course of the three funding periods.
In the first funding period the mechanical principles to control damage are to be worked out. An analysis of the impact of the model parameters (geometry, boundary conditions) on the structural behavior (deformation, damage, stresses) within the scope of variational sensitivity analysis (first variation, then discretization) is crucial. Well-known damage criteria (e.g. Cockroft/Latham), classical damage models (Lemaitre, Gurson/Tvergaard/Needleman) as well as the new developments from project C02 are to be covered. The novelty of this project is the variational sensitivity analysis and the corresponding structural optimization of anisotropic plasticity, anisotropic damage, and gradient-enhanced damage modeling regarding the variation of geometry and boundary conditions. Innovative, too, is the singular value decomposition (SVD) of the above-mentioned models’ sensitivity information that allows a quantitative determination of the most important parameters and the refinement (reduction) of the optimization problem. On this basis, fundamental optimization problems on mechanical comprehension of damage are treated. Exemplary, (i) the determination of optimal load paths to minimize damage and (ii) the minimization of damage by shape changes of the component can be mentioned for chosen academic demonstrators.
The aim of the second funding period is the consideration of complex forming processes, e.g. of sheet metals, in sensitivity analysis and optimization.
The aim of the third funding period is the junction of knowledge to a general optimization strategy. An optimization algorithm, applicable for the industry, for the purpose of multi-objective optimization shall control damage during the industrial forming process and allow the construction of a component with the aim of a maximized service life.
Project leader
Prof. Dr.-Ing. Franz-Joseph Barthold
Chair of Structural Mechanics (BM), TU Dortmund University
Project coordinator
Fabian Guhr M. Sc.
Chair of Structural Mechanics (BM), TU Dortmund University
