Composite materials have been an area of active research in recent years due to the possibility of obtaining multifunctional structures. Viscoelastic layered composites with parallel plane layers consisting of a stiff constituent and a soft viscoelastic constituent are of particular interest as they have been shown to exhibit simultaneous high stiffness and high damping. Such materials would be useful in structural applications and in high vibration environments such as in a vehicle or machinery. They would provide the rigidity required while simultaneously dissipating mechanical energy. The finite deformation mechanics of parallel plane viscoelastic layered composites has not been extensively studied. Under compressive loads they are very susceptible to instabilities. Buckling, for example is an elastic instability seen in load bearing materials. Since viscoelastic materials are rate and time dependent, the buckling modes for these composites not only depend on these factors, but also on the volume fraction of the stiff constituent. Three different cases are identified in the buckling and post-buckling response of these composites: non-dilute (high volume fraction), transition (intermediate volume fraction) and dilute (small volume fraction) cases. Due to buckling from the application of prestrain, the stiffness and damping of these composites can be tuned by orders of magnitude. Adaptive and multifunctional materials can be designed taking advantage of this idea and the rate dependence of the modes of deformation.

In this thesis, first a higher order dynamic theory for anisotropic thermoelastic plates is developed. Then, based on this plate theory, two dynamic models, discrete and continuum models (DM and CM), are proposed for layered composites consisting of anisotropic thermoelastic layers. Of the two models, CM is more important, which is established in the study of periodic layered composites using smoothing operations. CM has the properties: it contains inherently the interface and Floquet conditions and facilitates the analysis of the composite, in particular, when the number of laminae in the composite is large / it contains all kinds of deformation modes of the layered composite / its validity range for frequencies and wave numbers may be enlarged by increasing, respectively, the orders of the theory and interface conditions. CM is assessed by comparing its prediction with the exact for the spectra of harmonic waves propagating in various directions of a two-phase periodic layered composite, as well as, for transient dynamic response of a composite slab induced by waves propagating perpendicular to layering. A good comparison is observed in the results and it is found that the model predicts very well the periodic structure of spectra with passing and stopping bands for harmonic waves propagating perpendicular to layering. In view of the results, the physical significance of Floquet wave number is also discussed in the study.

Functionally graded materials (FGMs) are an advanced class of material which seeks to leverage the strengths of one material to mitigate the weaknesses of another. This allows for operation in extreme environments or conditions where materials properties must change at various locations within a structure. Fabrication of this advanced class of material is limited due to geometric, economic, and material constraints inherent in the various methods. For this reason, a model was developed to discretize continuous gradient curves to allow for the use of a step-wise approximations to such gradients. These alternative step-wise gradients would allow for the use of numerous manufacturing techniques which have improved composition control, cost of processing, cost of equipment, and equipment availability. One such technique, tape casting, was explored due to its robustness and ability to create layered ceramics. Since ceramics are inherently brittle materials, they serve to be strengthened by the thermal residual stresses that form in the creation of these step-wise graded composites. With models to calculate these residual stresses and determine step-wise approximations of various compositional gradients, the process of designing these layered ceramics can be significantly improved.

Disertační práce se zabývá mechanickou odezvou vrstevnatých kompozitů pro stomatologické aplikace. Různé skladby vrstev a různé částicové a vláknové kompozity jsou studovány v tříbodovém ohybu za pokojové teploty. Tyto výsledky jsou korelovány s výstupy dynamické termomechanické analýzy (DMTA) a optické analýzy (vysokorychlostní video záznam, SEM). Exeprimentální data byla použita pro srovnání s výsledky analytických a numerických modelů s cílem určit nejvhodnější model pro predikci základních mechanických vlastností vrstevnatých kompozitů. Na základě těchto analýz jsou navržena základní pravidla pro klinické použití vrstevnatých kompozitů ve stomatologických aplikacích jako jsou minimálně invazivní můstky nebo stabilizační dlahy.