A continuous material law for modeling thin-sheet piles and their frictional connection

In the present paper, the mechanical modeling and the numerical simulation of a pile of thin sheets under compressive and in-plane forces is presented. These sheets are not glued or laminated, but interact through frictional contact only. In applications, as for example the core of a large power transformer, such piles may consist of thousands of sheets, which are of thickness below 1 mm, while the dimensions of the pile reaches several meters. Also, several piles may interact by a frictional connection. Such connections are realized by regions where sheets from both stacks overlap mutually. Simulations using a properly meshed original geometry and standard finite element models lead to billions of unknowns for industrial applications. Additionally, the system is highly nonlinear due to the heavily coupled contact conditions posed on thousands of interfaces. Simulations become extremely expensive in terms of both memory and computation time, if not even unsolvable due to numerical convergence problems. The aim of this paper is to present a macroscopic material model, which can be applied to an equivalent homogenized computational domain representing the interconnected sheet piles. An extension of the material law in regions of mutual overlapping due to frictional connections is provided. When using the present approach, the homogenized computational domain can be discretized by a far smaller number of unknowns, while a good overall accuracy is retained. The numerical solution of standardized test problems is presented and verified against analytical considerations.