Lattice materials are used as the core of sandwich panels to construct light and strong structures. This thesis focuses on metallic sandwich structures and has two main objectives: (i) explore how a surface treatment can improve the strength of a lattice material and (ii) investigate the collapse response of two competing prismatic sandwich cores employed in ship hulls. First, the finite element method is used to examine the effect of carburisation and strain hardening upon the compressive response of a pyramidal lattice made from hollow tubes or solid struts. The carburisation surface treatment increases the yield strength of the material, but its effects on pyramidal lattices are not known. Here, it is demonstrated that carburisation increases the plastic buckling strength of the lattice and reduces the slenderness ratio at which the transition from plastic to elastic buckling occurs. The predictions also showed that strain hardening increases the compressive strength of stocky lattices with a slenderness ratio inferior to ten, but without affecting the collapse mode of the lattice. Second, the quasi-static three-point bending responses of simply supported and clamped sandwich beams with a corrugated core or a Y-frame core are compared via experiments and finite element simulations. The role of the face-sheets is assessed by considering beams with (i) front-and-back faces present and (ii) front face present, but back face absent. These two beam designs are used to represent single hull and double hull ship structures, and they are compared on an equal mass basis by doubling the thickness of the front face when the back face is absent. Beams with a corrugated core are found to be slightly stronger than those with a Y-frame core, and two collapse mechanisms are identified depending upon beam span. Short beams collapse by indentation and for this collapse mechanism, beams without a back face outperform those with front-and back faces present. In contrast, longbeams fail by Brazier plastic buckling and for this collapse mechanism, the presence of a back face strengthens the beam. Third, drop weight tests with an impact velocity of 5 m/s are performed on simply supported and clamped sandwich beams with a corrugated core or a Y-frame core. These tests are conducted to mimic the response of a sandwich hull in a ship collision. The responses measured at 5 m/s are found to be slightly stronger than those measured quasi-statically. The measurements are in reasonable agreement with finite element predictions. In addition, the finite element method is used to investigate whether the collapse mechanism at 5 m/s is different from the one obtained quasi-statically. The predictions indicate that sandwich beams that collapse quasi-statically by indentation also fail by indentation at 5 m/s. In contrast, the simulations for beams that fail quasi-statically by Brazier plastic buckling show that they collapse by indentation at 5 m/s. Finally, the dynamic indentation response of sandwich panels with a corrugated core or a Y-frame core is simulated using the finite element method. The panels are indented at a constant velocity ranging from quasi-static loading to 100 m/s, and two indenters are considered: a flat-bottomed indenter and a cylindrical roller. For indentation velocities representative of a ship collision, i.e. below 10 m/s, the predictions indicate that the force applied to the front face of the panel is approximately equal to the force transmitted to the back face. Even at such low indentation velocities, inertia stabilisation effects increase the dynamic initial peak load above its quasi-static value. This strengthening effect is more important for the corrugated core than for the Y-frame core. For velocities greater than 10 m/s, the force applied to the front face exceeds the force transmitted to the back face due to wave propagation effects. The results are also found to be very sensitive to the size of the flat-bottomed indenter; increasing its width enhances both inertia stabilisation and wave propagation effects. In contrast, increasing the roller diameter has a smaller effect on the dynamic indentation response. Lastly, it is demonstrated that material strain-rate sensitivity has a small effect on the dynamic indentation response of both corrugated and Y-frame sandwich panels.

Cellular materials, often called lattice materials, are increasingly receiving attention for their ultralight structures with high specific strength, excellent impact absorption, acoustic insulation, heat dissipation media and compact heat exchangers. In alignment with emerging additive manufacturing (AM) technology, realization of the structural applications of the lattice materials appears to be becoming faster. Considering the direction dependent material properties of the products with AM, by directionally dependent printing resolution, effective moduli of lattice structures appear to be directionally dependent. In this paper, a constitutive model of a lattice structure, which is an octet-truss with a base material having an orthotropic material property considering AM is developed. In a case study, polyjet based 3D printing material having an orthotropic property with a 9% difference in the principal direction provides difference in the axial and shear moduli in the octet-truss by 2.3 and 4.6%. Experimental validation for the effective properties of a 3D printed octet-truss is done for uniaxial tension and compression test. The theoretical value based on the micro-buckling of truss member are used to estimate the failure strength. Modulus value appears a little overestimate compared with the experiment. Finite element (FE) simulations for uniaxial compression and tension of octet-truss lattice materials are conducted. New effective properties for the octet-truss lattice structure are developed considering the observed behavior of the octet-truss structure under macroscopic compression and tension trough simulations.

The static and dynamic response of lattice materials is investigated to disclose and control the connection between microstructure and effective behavior. The analytical methods developed in the thesis aim at providing a new understanding of material instabilities and strain localizations as well as effective tools for controlling wave propagation in lattice structures. The time-harmonic dynamics of arbitrary beam lattices, deforming flexurally and axially in a plane, is formulated analytically to analyze the influence of the mechanical parameters on the dispersion properties of the spectrum of Floquet-Bloch waves. Several forms of dynamic localizations are shown to occur for in-plane wave propagation of grid-like elastic lattices. It is demonstrated that lattices of rods, despite being `simple' structures, can exhibit a completely different channeled response depending on the characteristics of the forcing source (i.e. frequency and direction) as well as on the slenderness of the elastic links. It is also shown how the lattice parameters can be tuned to attain specific dispersion properties, such as flat bands and sharp Dirac cones. In the research field of material instabilities, a key result proposed in this thesis is the development of both static and dynamic homogenization methods capable of accounting for second-order effects in the macroscopic response of prestressed lattices. These methods, the former based on an incremental strain-energy equivalence and the latter based on the asymptotic analysis of lattice waves, allow the identification of the incremental constitutive operator capturing the macroscopic incremental response of arbitrary lattice configurations. The homogenization framework has allowed the systematic analysis of prestress-induced phenomena on the incremental response of both the lattice structure and its `effective' elastic solid, which in turn has enabled the identification of the complex interplay between microstructure, prestress, loss of ellipticity (shear band formation) and short-wavelength bifurcations. Potential new applications for the control of wave propagation are also shown to be possible by leveraging the inclusion of second-order terms in the incremental dynamics. In particular, the tunability of the prestress state in a square lattice structure has been exploited to obtain dynamic interfaces with designable transmission properties. The interface can be introduced in a material domain by selectively prestressing the desired set of ligaments and the prestress level can be tuned to achieve total reflection, negative refraction, and wave channeling. The obtained results open new possibilities for the realization of engineered materials endowed with a desired constitutive response, as well as to enable the identification of novel dynamic material instabilities.