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DFG-Schwerpunktprogramm 1146: Modellierung inkrementeller Umformverfahren

Project manager: Prof. Dr. rer. nat. B. I. Wohlmuth
Projektbearbeiter: Dr. E. Savenkov

Initial Situation

The project is devoted to the development and implementation of the efficient methods of the solution of complex coupled problems of contact and plasticity, applied to the incremental metal sheet forming process.

Incremental metal sheet forming process is a quite new engineering technology, which allows to obtain efficiently a geometrically complex forms. Practical applications of this method are very important and it is studied quite extensively in experiments.

The goal of the project is development of the algorithms, which would allow simulate the process, taking all important physical issues into account.

The chosen approach is based on overlapping domain decomposition method. Such choice is motivated by the fact, that the size of the working tool is sufficiently smaller, then the size of the working piece (i.e., the formed sheet). The main components of the model at the moment are plasticity in the working piece and accurate treatment of the contact between the tool and the sheet. Nonlinear (due to plasticity and contact) problem is solved only inside small patch (which size is of the order of the working tool), and only linear problem on the coarse mesh is solved inside the global domain. The data transfer between overlapping volume and surface meshes is organized using corresponding mortar coupling operators. As soon as working tool moves over working piece, the fine mesh follows it. Therefor, the efficient and robust data transfer is one of the main requirements of the method.

Current Results

The current work was devoted to the extension of the earlier developed algorithms to more general cases.

In particular, the method was extended for the case of several working tools, which moves simultaneously inside domain. Every working tool has its own fine subdomain; the paths of the tools are completely independent.

Since the fine meshes moves, generally, following the arbitrary predefined path, one of the important ingredients of the method is efficient mortar coupling. This concerns, first of all, volumetric mortar coupling, which is used to transfer loadings and plastic history data between fine and coarse meshes. To do this, a new mortar operators based on the dual Lagrange multipliers approach were developed. The distinguishing feature of these operators is that they allow to transfer data directly between Gauss points of the different meshes. This allows to avoid the usage of expensive and dissipative mesh transfer operators still widely used in practice, i.e., there is no Gauss points to mesh nodes (re)-interpolation is needed.

Work Plan

The future work will be focused preliminary on the extension of the model and earlier developed approaches in order to take heating effects into account. The already developed model will be extended with the heat equation, which will be coupled with plasticity model in use.

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