Influence of boundary conditions on the response of multilayered plates with cohesive interfaces and delaminations using a homogenized approach

摘要

Stress and displacement fields in multilayered composites with interfacial imperfections, such asimperfect bonding of the layers or delaminations, or where the plies are separated by thin interlayers allowingrelative motion, have large variations in the thickness, with characteristic zigzag patterns and jumps at the layerinterfaces. These effects are well captured by a model recently formulated by the author for multilayered plateswith imperfect interfaces and affine interfacial traction laws (Massabò & Campi, Meccanica, 2014, in press; ComposStruct, 2014, 116, 311-324). The model defines a homogenized displacement field, which satisfies interfacialcontinuity, and uses a variational technique to derive equilibrium equations depending on only six generalizeddisplacement functions, for any arbitrary numbers of layers and interfaces. The model accurately predictsstresses and displacements in simply supported, highly anisotropic, thick plates with continuous, slidinginterfaces. In this paper the model is applied to wide plates with clamped edges and some inconsistencies, whichhave been noted in the literature for models based on similar approaches and have limited their utilization, areexplained. A generalized transverse shear force is introduced as the gross stress resultant which is directlyrelated to the bending moment in the equilibrium equations of multilayered structures with imperfect interfacesand substitutes for the shear force of single-layer theory. An application to a delaminated wide plate highlightsthe potential and limitations of the proposed model for the solution of fracture mechanics problems.