Until recently, the analysis of polymer laminates using infrared microspectroscopy involved the painstaking separation of individual layers by dissection or by obtaining micrometer thin cross-sections. The latter usually requires the expertise of an individual trained in microtomy and even then, the very structure of the laminate could affect the outcome of the spectral results. The recent development of attenuated total internal reflection (ATR) infrared microspectroscopy imaging has provided a new avenue for the analysis of these multilayer structures. This report compares ATR infrared microspectroscopy imaging with conventional transmission infrared microspectroscopy imaging. The results demonstrate that the ATR method offers improved spatial resolution, eliminates a variety of competing optical processes, and requires minimal sample preparation relative to transmission measurements. These advantages were illustrated using a polymer laminate consisting of 11 different layers whose thickness ranged in size from 4–20 μm. The spatial resolution achieved by using an ATR-FTIR (Fourier transform infrared spectroscopy) imaging technique was diffraction limited. Contrast in the ATR images was enhanced by principal component analysis.

The stability behavior of the Leipholz’s type of laminated box columns with nonsymmetric lay-ups resting on elastic foundation is investigated using the finite element method. Based on the kinematic assumptions consistent with the Vlasov beam theory, a formal engineering approach of the mechanics of the laminated box columns with symmetric and nonsymmetric lay-ups is presented. The extended Hamilton’s principle is employed to obtain the elastic stiffness and mass matrices, the Rayleigh damping and elastic foundation matrices, the geometric stiffness matrix due to distributed axial force, and the load correction stiffness matrix accounting for the uniformly distributed nonconservative forces. The evaluation procedures for the critical values of divergence and flutter loads with/without internal and external damping effects are briefly presented. Numerical examples are carried out to validate the present theory with respect to the previously published results. Especially, the influences of the fiber angle change and damping on the divergence and flutter loads of the laminated box columns are parametrically investigated.

In this paper we study sharp localized ${{L}^{q}}\,\to \,{{L}^{p}}$ estimates for Fourier multipliers resulting from modulation of the jumps of Lévy processes. The proofs of these estimates rest on probabilistic methods and exploit related sharp bounds for differentially subordinated martingales, which are of independent interest. The lower bounds for the constants involve the analysis of laminates, a family of certain special probability measures on 2×2 matrices. As an application, we obtain new sharp bounds for the real and imaginary parts of the Beurling–Ahlfors operator.

In this paper we study the realizability of a given smooth periodic gradient field ∇u defined in Rd, in the sense of finding when one can obtain a matrix conductivity σ such that σ∇u is a divergence free current field. The construction is shown to be always possible locally in Rd provided that ∇u is non-vanishing. This condition is also necessary in dimension two but not in dimension three. In fact the realizability may fail for non-regular gradient fields, and in general the conductivity cannot be both periodic and isotropic. However, using a dynamical systems approach the isotropic realizability is proved to hold in the whole space (without periodicity) under the assumption that the gradient does not vanish anywhere. Moreover, a sharp condition is obtained to ensure the isotropic realizability in the torus. The realizability of a matrix field is also investigated both in the periodic case and in the laminate case. In this context the sign of the matrix field determinant plays an essential role according to the space dimension. The present contribution essentially deals with the realizability question in the case of periodic boundary conditions.

The use of composite laminates is increasing in these days due to desired directional properties and low densities in comparison of metals. Delamination is a major source of failure in composite laminates where a crack like entity can initiate and propagate between different layers of composite laminates under given loading conditions. Damage mechanics based theories are employed to simulate the delamination phenomena between composite laminates. These damage models are inherently local and can cause the concentration of stresses around the crack tip. In the present study integral type non-local damage formulation is proposed to avoid the localization problem associated to damage formulation. A comprehensive study is carried out for the selection of different non-local variables. Finite element simulations based on proposed non-local damage models and classical local damage model are performed and results are compared with available experimental data for UD IMS/924 Carbon/fiber epoxy composite laminate.

The temperature versus life (T-N) curves of both centrally notched and unnotched AS-4/PEEK (APC-2) composite laminates due to constant stress amplitude tension-tension (T-T) fatigue loading were investigated systematically. The cross-ply laminate possesses the higher mechanical properties than those of the quasi-isotropic laminate at elevated temperature, and also the mechanical properties of both lay-ups are degraded significantly as the temperature increasing. Combining both effects of notch and temperature at various normalized stresses it is found the cross-ply laminate possesses more resistance to cyclic loading than that of the quasi-isotropic laminate. Additionally, the predictive strain model is in a practical and simple form. Alternatively, the T-N curves, instead of conventionally S-N curves, at variously applied stresses are accomplished for preliminary designs and applications.