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The role of exchange interactions in the dynamics of collective excitations in magnetic materials is of essential importance, and since the experimental discovery of planar ferromagnetism, a flurry of research has rapidly reshaped the field of 2D materials. Although this topic has been widely addressed, the direct effects of exchange interactions on controlling the energy distribution of ferromagnetic systems, via the dispersion relationship, have not been adequately explored. This work investigates this theme and analyzes the repercussions on the magnonic density of states and energy fluctuations in the high symmetry paths of a ferromagnetic lattice with honeycomb topology, which made it possible to determine the points and direction most sensitive to this type of interaction.

Conventional bending-dominated lattices exhibit less specific stiffness compared to stretching-dominated lattices while showing high specific energy absorption capacity. This paper aims to improve the specific stiffness of bending-dominated lattices by introducing elementary-level programmed curvature through a multilevel hierarchical framework. The influence of curvature in the elementary beams is investigated here on the effective in-plane and out-of-plane elastic properties of lattice materials. The beamlike cell walls with out-of-plane curvature are modeled based on three-dimensional degenerated shell finite elements. Subsequently, the beam deflections are integrated with unit cell level mechanics in an efficient semi-analytical framework to obtain the lattice-level effective elastic moduli. The numerical results reveal that the effective in-plane elastic moduli of lattices with curved isotropic cell walls can be significantly improved without altering the lattice-level relative density, while the effective out-of-plane elastic properties reduce due to the introduction of curvature. To address this issue, we further propose laminated composite cell walls with out-of-plane curvature based on the three-dimensional degenerated shell elements, which can lead to holistic improvements in the in-plane and out-of-plane effective elastic properties. The proposed curved composite lattice materials would enhance the specific stiffness of bending-dominated lattices to a significant extent, while maintaining their conventional multifunctional advantages. [ABSTRACT FROM AUTHOR]

The homogenized classical and higher-order mechanical properties of repetitive lattice materials are evaluated using Timoshenko beam models at a microlevel, and a continualization method towards a Cosserat homogenized substitution medium is applied. The proposed method combines a reduced number of degrees of freedom at a unit cell level with the continuous set of kinematic variables, which are representative of a Cosserat continuum at the macroscale. The homogenized classical and Cosserat moduli are obtained as closed-form expressions of the lattice microstructural and mechanical parameters for the specific case of honeycomb lattices. The proposed continualization method proves to be accurate and computationally efficient in comparison with fully resolved finite element simulations. One main hallmark of this paper is the quantification of edge effects in the response of lattice structures, relying on the surface formulation of the extended Hill macrohomogeneity condition. The bending moment to curvature relation involves a classical term and a micropolar bending moment, the importance of which is decreasing asymptotically up to a nil value by increasing the number of unit cells in the height of the macrostructure. [ABSTRACT FROM AUTHOR]