Related papers: New examples of three-dimensional dilational mater…
We outline our work (see [1,2,3,4]) on relaxation and 3d-2d passage with determinant type constraints. Some open questions are addressed. This outline-paper comes as a companion to [5].
This article deals with 3-forms on 6-dimensional manifodls, the first dimension where the classification of 3-forms is not trivial. There are three classes of multisymplectic 3-forms there. We study the class which is closely related to…
Flexible mechanical metamaterials are compliant structures engineered to achieve unique properties via the large deformation of their components. While their static character has been studied extensively, the study of their dynamic…
The paper considers rotations at different scales in granular materials: the rotations of individual particles, the rolling and rigid-rotation of particle pairs, the rotational interactions of a particle within its cluster of neighbors, and…
The field of two-dimensional topological semimetals, which emerged at the intersection of two-dimensional materials and topological materials, have been rapidly developing in recent years. In this article, we briefly review the progress in…
Simple deformations, with a parameter $\epsilon$, of classical $R$-matrices which follow from decomposition of appropriate Lie algebras, are considered. As a result nonstandard Lax representations for some well known integrable systems are…
A convection-diffusion problem with a large shift in space is considered. Numerical analysis of high order finite element methods on layer-adapted Duran type meshes, as well as on coarser Duran type meshes in places where weak layers…
We describe a method for modeling the geometry of porous materials. The approach enables the independent selection of crucial parameters, including porosity, pore size distribution, pore shape, and connectivity. Consequently, it can…
In this article, we find finitely many numerical invariants to classify the diffeomorphism types of three dimensional simply connected Mori fibre spaces with torsion free homology groups.
Review of selected fundamental topics on the interaction between phase transformations, fracture, and other structural changes in inelastic materials is presented. It mostly focuses on the concepts developed in the author's group over last…
We investigate a minimal model of the plastic deformation of amorphous materials. The material elements are assumed to exhibit ideally plastic behavior (J2 plasticity). Structural disorder is considered in terms of random variations of the…
We study the self-healing process of materials with embedded "glue"-carrying cells, in the regime of the onset of the initial fatigue. Three-dimensional numerical simulations within the percolation-model approach are reported. The main…
Carbon has numerous one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) allotropic structures. The study of carbon materials has been a major focus of material science and condensed matter physics. Previous studies have…
First-principles studies of two-dimensional transition metal dichalcogenides have contributed considerably to the understanding of their dielectric, optical, elastic, and vibrational properties. The majority of works to date focus on a…
One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set $K$ in the plane or in space. The most commonly used measure of efficiency is density. Several types of…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
We present fully three-dimensional equations to describe the rotations of a body made of a deformable mantle and a fluid core. The model in its essence is similar to that used by INPOP (Integration Plan\'{e}taire de l'Observatoire de…
We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes…
Deployable structures, essential across various engineering applications ranging from umbrellas to satellites, are evolving to include soft, morphable designs where geometry drives transformation. However, a major challenge for soft…
Two-dimensional (2D) materials are among the most promising candidates for beyond-silicon electronic, optoelectronic and quantum computing applications. Recently, their recognized importance sparked a push to discover and characterize novel…