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C. Adam, F. Ziegler:
"Vibrations of layered beams under conditions of damaging and slipping interfaces";
International Journal of Fracture (invited), 98 (1999), 3-4; 393 - 406.

A nonlinear laminate layerwise beam theory is developed to simulate the effect of inelastic interlayer slip on the stiffness degradation of layered beam structures. Layerwise continuous and linear in-plane displacement fields are implemented. It is shown that by definition of an effective cross-sectional rotation the complex problem reduces to the simpler case of a homogenized shear-deformable beam with effective stiffness and a corresponding set of boundary conditions. Inelastic defects of the interlayer material are equivalent to eigenstrains in an identical but unlimited elastic background structure of the homogenized beam with proper effective virgin stiffness. Cross-sectional resultants of these eigenstrains are defined. Since the incremental response of the background to the given load and to the properly, in space and time updated, imposed eigenstrain increments is considered to be linear within a given time step, effective solution methods of the linear theory of flexural vibrations become applicable.

A nonlinear laminate layerwise beam theory is developed to simulate the effect of inelastic interlayer slip on the stiffness degradation of layered beam structures. Layerwise continuous and linear in-plane displacement fields are implemented. It is shown that by definition of an effective cross-sectional rotation the complex problem reduces to the simpler case of a homogenized shear-deformable beam with effective stiffness and a corresponding set of boundary conditions. Inelastic defects of the interlayer material are equivalent to eigenstrains in an identical but unlimited elastic background structure of the homogenized beam with proper effective virgin stiffness. Cross-sectional resultants of these eigenstrains are defined. Since the incremental response of the background to the given load and to the properly, in space and time updated, imposed eigenstrain increments is considered to be linear within a given time step, effective solution methods of the linear theory of flexural vibrations become applicable.