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Boundary layers stresses in elastic composites. (English) Zbl 0621.73017
Local effects in the analysis of structures, EUROMECH Colloq., Cachan/France 1984, Stud. Appl. Mech. 12, 215-232 (1985).
[For the entire collection see Zbl 0618.00012.]
We consider an elastic stratified material with a periodic structure and we calculate the local stresses near a free boundary. Assuming that the microscopic displacements and stresses are periodic in the direction of the stratification, an homogenization method gives an approximation of the micro-stresses within the material. Since this approximation is not valid in the neighbourhood of the boundary, we define new micro-stresses as the sum of the microscopic stresses of the classical homogenization and boundary layers stresses which are periodic parallel to the boundary. These additional stresses satisfy a well-posed problem and decrease exponentially with the orthogonal boundary variable. We present some numerical results, which show the improvement in the stress calculation specially near the boundaries. This method gives also good results with other composite materials and with other types of boundary conditions.

74E05 Inhomogeneity in solid mechanics
35R35 Free boundary problems for PDEs