A two-dimensional homogenized model for a pile of thin elastic sheets with frictional contact

Abstract

The present paper deals with the computational simulation of a pile of thin sheets. The sheets are not laminated or glued, but they interact by frictional contact. In general, it is not possible to perform a full-scale finite element contact computation for piles containing thousands of sheets; the problem size becomes too large, and numerical solution methods suffer from severe convergence problems due to the large number of strongly coupled contact conditions. In this paper, a macroscopic material model is presented for the two-dimensional case. The pile of sheets is homogenized by introducing an effective anisotropic constitutive law, which is motivated by formulations of the theory of elasto-plasticity. This macroscopic material law models the behavior of a pile of sheets, allowing for no tensile stresses in the direction normal to the sheets and obeying Coulomb’s law of friction in the tangential contact plane. Applying this macroscopic material model, an equivalent homogeneous body can be treated using much coarser discretizations. Computational results for the problems are provided, and a comparison with simplified contact computations is done.