Global-Local Laminate Variational Model
The absence of a unified, tractable model to predict the elastic response of a multi-layered laminate (say 100 layers) has foiled attempts to understand the failure modes of practical composite structures. Global models, which follow from an assumed displacement field and lead to the definition of effective (or smeared) laminate moduli, are not sufficiently accurate for stress field computation. On the other hand, local models, in which each layer is represented as a homogeneous anisotropie continuum, become intractable as the number of layers becomes even moderately large (approx. l0). In this work, we blend these concepts into a self-consistent model which can define detailed response functions in a region of interest (local), while representing the remainder of the domain by effective properties (global). In this investigation the laminate thickness is divided into two parts. A variational principle has been used to derive the governing equations of equilibrium. For the global region of the laminate, potential energy has been utilized, while the Reissner functional has been used for the local region. The field equations are based upon an assumed thickness distribution of stress components within each layer of the local region and displacement components in the global region. The derived boundary conditions imply that the computed stress field on the surfaces of the global region and the prescribed tractions (point wise in an elasticity sense) satisfy the conditions of vanishing resultant force and moment identically. The same conditions are satisfied in the local region. The stress fields obtained by this formulation compare very well with those obtained by other approaches for laminates with a small number of layers. For large number of layers, internally consistent results are achieved by varying the representation of the global region in the present model.
KeywordsStress Component Composite Laminate Edge Condition Global Region Local Domain
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