Mechanical and Thermal Properties of 2D Materials

We study dynamical phenomena in a harmonic graphene (honeycomb) lattice, consisting of equal particles connected by linear and angular springs. Equations of in-plane motion for the lattice are derived. Initial conditions typical for molecular dynamic modeling are considered. Particles have random initial velocities and zero displacements. In this case, the lattice is far from thermal equilibrium. In particular, initial kinetic and potential energies are not equal.

Moreover, initial kinetic energies (and temperatures), corresponding to degrees of freedom of the unit cell, are generally different. The motion of particles leads to the equilibration of kinetic and potential energies and redistribution of kinetic energy and corresponding temperature among degrees of freedom. During equilibration, the kinetic energy performs decaying high-frequency oscillations. We show that these oscillations are accurately described by an integral depending on the dispersion relation and polarization matrix of the lattice. At large times, kinetic and potential energies tend to equal values. Kinetic energy is partially redistributed among degrees of freedom of the unit cell. Equilibrium distribution of the kinetic energies is accurately predicted by the non-equipartition theorem. Presented results may serve for a better understanding of the approach to thermal equilibrium in graphene.

Coarse-Grained and Atomic Modeling of Single-Layered Molybdenum Disulfide

Single-layered molybdenum disulfide is a novel 2D material having a great potential application in nanoelectronics. In our recent work, we developed a novel potential of interaction for atoms of molybdenum and silicon based on torque interactions. The topic of the current investigation is devoted to the development of coarse-grained models of layered nanomaterials. Similarly to ab initio or molecular dynamics approaches, coarse-grained models take the microstructure of the crystal lattice into account.

However, unlike the above-mentioned approaches, the structural elements (particles) correspond not to atoms of the crystal lattice, but to some periodic grains. As a result, an increase of the particle used to simulation experiments leads to a decrease of the particles and speeds up the computations. The main problem is to choose the optimal grains and to determine the potential of interaction between them. The method was applied to calculate the phonon spectrum and simulate the nanoindentation of SLMoS2.

Mechanical Properties of Graphene and Simple Crystal Lattices

We develop discrete models of graphene and some other crystal lattices considering multibody potentials of interaction between carbon atoms, torques-based potentials of interaction and structural models of graphene interatomic bond. On a macroscale, the crystal lattice is represented as classical or micropolar effective continua. We determine the effective properties of the lattice using its geometry and parameters of interatomic interaction in the bonds.

A bending rigidity of graphene and triangular lattice were determined based on torque interaction model. Also, we considered the dynamical properties of graphene and triangular crystal lattice. For graphene lattice, the dispersion relations were determined based on multibody potential and Floquet-Bloch analysis. For triangular crystal lattice, new analytical solutions were obtained to describe localized non-linear strain waves.

Mechanical Properties of Artificial Materials

Artificial materials include periodic structures, acoustic metamaterials, nanocomposites, etc. These materials have a wide application in mechanical engineering, aerospace technology, electronics and other areas due to their outstanding properties based on properties of combined materials (as for nanocomposites) or on the exactingly-designed structure (as for metamaterials).

A special class of materials and structures expanding in one or more directions when strained along the other direction is called ‘auxetic’. We study elastic properties of cellular lattice materials are studied using the discrete models. The models are based on a representation of the lattice as a set of interacting nodes. A potential of interaction between the nodes is calibrated such that to simulate elastic linking. As a result, the problems of analytic and computational homogenization, crack propagation, and shape-changing large strains are solved.

Mechanics of Nacre-Like Material

Recently, nacre-like materials raised the interest of scientists. Such a brick and mortar microstructure, characterized by stiff elements of one phase with a high aspect ratio separated by thin layers of the second one, is proved to provide an efficient solution for the problem of a crack arrest. As a result, full-scale continuum modeling of both composite constituents without employing any simplifying assumptions was presented.

Mechanics of Hydrogels

We investigated the mechanical properties of the fibrin-based hydrogel at the macro and micro levels. On a macrolevel, a finite element model of the stiff ball – soft hydrogel contact was developed. A hydrogel was modeled using the non-linear hyperelastic models. The parameters of the models were determined based on the experimental data.

Our next step is to create the hydrogel model at the microscopic level, which will also correlate with the experimental data. This model will simulate the network of fibers. Each fibril will be described by a nonlinear elastic material. The entire network of fibrils will be immersed in a viscous medium.

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