Abstract
Equivalent single layer theories for layered beams effectively and accurately predict global displacements and internal force and moment resultants using a limited number of displacement variables. However, they cannot reproduce local effects due to material architecture or weak/imperfect bonding of the layers, such as zigzag displacement fields, displacement jumps at the layer interfaces and complex transverse stress fields, nor can they simulate delamination damage growth. In this work we will present some applications and discuss advantages and limitations of a recently formulated zigzag model. The model, through a modification of the equilibrium equations of an equivalent single layer theory, which maintains the same number of variables, reproduces local effects and delamination fracture under mode II dominant conditions. The approach is based on a local enrichment of the displacement field of first order shear deformation theory, the introduction of cohesive interfaces and homogenization.
Highlights
The mechanical response of layered structures, such as laminates, sandwich composites, laminated glass, and laminated wood, is controlled by local effects due to the elastic mismatch of the layers, the presence of thin interlayers, and interfacial imperfections, defects and delaminations, which are typical consequences of manufacturing processes
The homogenized model uses a zigzag kinematic approximation based on first order shear deformation theory (FSDT) which is enriched by local zigzag functions and interfacial jumps, as shown in Eqn (1)
A homogenized structural model based on a zigzag approach has been presented for the analysis of beams with imperfect interfaces and delaminations and layers oriented along the geometrical axes
Summary
The mechanical response of layered structures, such as laminates, sandwich composites, laminated glass, and laminated wood, is controlled by local effects due to the elastic mismatch of the layers, the presence of thin interlayers (adhesives, resin rich regions, polymeric layers), and interfacial imperfections, defects and delaminations, which are typical consequences of manufacturing processes. Delamination damage evolution in the beam can be studied by releasing the displacement continuity at the layer interfaces and introducing cohesive interfacial tractions, normal and tangential, and cohesive traction laws which relate the tractions to the relative sliding and opening displacements [2,3,4] This approach requires 3n unknowns for each beam region (or (2n+1) unknowns for mode II dominant problems, where crack opening is neglected and a single displacement variable describes the transverse displacements of the layers). Zigzag functions and displacement jumps are defined by imposing continuity of transverse shear and normal tractions at the layer interfaces and the interfacial constitutive laws to relate tractions and jumps This yields the macro-scale displacement field and homogenized equilibrium equations which depend on the global variables only. The constitutive equations of the homogenized beam have been derived in [18]:
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