The ever-increasing demand for identifying materials with better functionality, drives the current trend in material's research. Several applications in the aerospace, defense, and sports industries require the materials to have high stiffness, decent damping, high toughness, and impact resistance. Such demand gives rise to the concept of creating architecture at multiple length scales within a ... [Show full abstract] structural material. The focus of this dissertation is on the (i) design based on the deformation mechanics, and failure of fully dense architectured materials where the individual building blocks are geometrically interlocked, and (ii) an interface constitutive model to predict rate dependent fracture of polymeric interfaces. Starting with a brief introduction in Chapter 1, the possibility of improving both the stiffness and energy absorption in interlocking, architectured, brittle polymer blocks is investigated in Chapter 3. The interlocking mechanism allows load transfer between two different material blocks by means of contact at the mating surfaces. The contacting surfaces further act as weak interfaces that allow the polymer blocks to fail gradually under different loading conditions. Such controlled failure enhances the energy absorption of the polymer blocks but with a penalty in stiffness. It is seen from finite element simulations and experiments that incorporating hierarchy in the form of another degree of interlocking at the weak interfaces, improves stress transfer between contacting material blocks, thereby, improvement in terms of stiffness and energy absorption is achieved. In Chapter 3, a naturally inspired ``interconnection" is considered within a composite material made of dissimilar mechanical properties with an objective to improve stiffness, toughness, and wave attenuation capability. The computational study showed that creation of weak interfaces along with the ``interconnection" works two-fold in terms of mechanical property improvement. The interconnection provides an additional load-transfer mechanism through contact-friction between two dissimilar materials, whereas the cohesive (weak) interfaces results in higher toughness (area under the stress-strain curve) of the material promoting distributed interface failure and delaying bulk material yielding. It was further identified that the presence of weak interfaces acts better in wave attenuation for the proposed composite. In Chapter 4, a new interface constitutive model is proposed to study rate-dependent, mixed-mode interface failure for polymeric adhesives. The model accounts for both reversible elastic as well as irreversible rate dependent separation-sliding deformation at the interface. The underlying assumption is that the viscous dissipation and the irreversible separation-sliding deformation at the interface can be modeled using an elastic-viscoplastic framework. The constitutive model is implemented in a commercial finite element code following an explicit scheme. A reasonable agreement has been found between finite element simulations and experimental observations, which reinstates the predictive capability of the proposed model for estimating the rate dependent response of polymer interfaces. Finally, few future recommendations have been provided in Chapter 5.