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We present a first-principles-based (second-principles) scheme that permits large-scale materials simulations including both atomic and electronic degrees of freedom on the same footing. The method is based on a predictive…
The paper addresses a novel model of metamaterial structure. A system of spinners has been embedded into a two-dimensional periodic lattice system. The equations of motion of spinners are used to derive the expression for the chiral term in…
This study examines the mechanical behavior of a novel class of mechanical metamaterials alternating pentamode lattices and stiffening plates. The unit cell of such lattices consists of a sub-lattice of the face cubic-centered unit cell…
We study convexity properties of energy functions in plane nonlinear elasticity of incompressible materials and show that rank-one convexity of an objective and isotropic elastic energy $W$ on the special linear group $\mathrm{SL}(2)$…
In recent years, the paradigm of `soft glassy matter' has been used to describe diverse nonergodic materials exhibiting strong local disorder and slow mesoscopic rearrangement. As so far formulated, however, the resulting `soft glassy…
Manufactured metallic components often contain non-uniformly distributed pores of complex morphologies. Since such porosity defects have significant influence on material behaviors and affect the usage in high-performance applications, it…
We present an analytical model to investigate the mechanics of 2-dimensional lattices composed of elastic beams of non-uniform cross-section. Our approach is based on reducing a lattice to a single beam subject to the action of a set of…
Moir\'e superlattice in two-dimensional (2D) materials provides a powerful platform to engineer emergent electronic states, yet the construction of moir\'e superlattices remains lab-scale, involving much trial and error and with little…
In this paper we study quantitative stochastic homogenization of a nonlinearly elastic composite material with a laminate microstructure. We prove that for deformations close to the set of rotations the homogenized stored energy function…
Geometrically frustrated magnetic systems, such as those based on the Shastry-Sutherland lattice (SSL), offer a rich playground for exploring unconventional magnetic states. The delicate balance between competing interactions in these…
Recent years have seen the discovery of systems featuring fragile topological states. These states of matter lack certain protection attributes typically associated with topology and are therefore characterized by weaker signatures that…
Applying elastic deformation can tune a material physical properties locally and reversibly. Spatially modulated lattice deformation can create a bandgap gradient, favouring photo-generated charge separation and collection in optoelectronic…
Starting from an energy comprised of both a bulk term and a surface term, set in the space of special functions of bounded hessian, $SBH$, a relaxation problem in the context of second-order structured deformations was studied in…
Since the discovery of graphene, intensive efforts have been made in search of novel two-dimensional (2D) materials. Decreasing the materials dimensionality to their ultimate thinness is a promising route to unveil new physical phenomena,…
New results are presented for the degeneracy condition of elastic waves in anisotropic materials. The existence of acoustic axes involves a traceless symmetric third order tensor that must vanish identically. It is shown that all previous…
Moir\'e effects in twisted or lattice-incommensurate vertical assemblies of two-dimensional crystals give rise to a new class of quantum materials with rich transport and optical phenomena, including correlated electron physics in flat…
Characterizing the long term behavior of dynamical systems given limited measurements is a common challenge throughout the physical and biological sciences. This is a challenging task due to the sparsity and noise inherent to empirical…
We propose a decomposition of constitutive relations into crack-driving and persistent portions, specifically designed for materials with anisotropic/orthotropic behavior in the phase field approach to fracture to account for the…
An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\ll1.$ A…
The classical problem of indentation on an elastic substrate has found new applications in the field of the Atomic Force Microscopy. However, linearly elastic indentation models are not sufficiently accurate to predict the…