Related papers: Structural parts as quadrics -- elasticity ellipse…
We formulate a phenomenological elasto-plastic theory to describe a solid undergoing a structural transition from a square (p4mm) to an oblique (p2) lattice in two dimensions. Within our theory, the components of the strain may be…
In this paper we classify and derive closed formulas for geometric elements of quadrics in rational B\'ezier triangular form (such as the center, the conic at infinity, the vertex and the axis of paraboloids and the principal planes), using…
Although for the most part classical, the topic of electrostatics finds to this day new applications. In this review we highlight several theoretical results on electrostatics, chosen to both illustrate general principles, and for their…
Elastic singularities such as crack tips, when in motion through a medium that is itself vibrating, are subject to forces orthogonal to the direction of motion and thus impossible to determine by energy considerations alone. This fact is…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…
Hierarchical structures are very common in Nature, but only recently have they been systematically studied in materials physics, in order to understand the specific effects they can have on the mechanical properties of various systems.…
Recent progress in approaches to determine the elastic constants of solids starting from the microscopic particle interactions is reviewed. On the theoretical side, density functional theory approaches are discussed and compared to more…
The theory, the design and the experimental validation of a catastrophe machine based on a flexible element are addressed for the first time. A general theoretical framework is developed by extending that of the classical catastrophe…
We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids, via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale $\xi_E$, so that the…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An…
We show that many well-known transforms in convex geometry (in particular, centroid body, convex floating body, and Ulam floating body) are special instances of a general construction, relying on applying sublinear expectations to random…
This work describes models and numerical approximations that describe the mechanical behavior of deformable continua with embedded structural members, such as rigid bodies, beams, shells, etc. The continuum formulation extends an idea first…
A formulation of Continuum Mechanics within the context of General Relativity is presented that allows for the incorporation of certain types of anelastic material behaviour, such as viscoelasticity and plasticity. The approach is based on…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…
In materials science, auxetic behavior refers to lateral widening upon stretching. We investigate the problem of finding domains of auxeticity in global deformation spaces of periodic frameworks. Case studies include planar periodic…
The Eshelbian (or configurational) force is the main concept of a celebrated theoretical framework associated with the motion of dislocations and, more in general, defects in solids. In a similar vein, in an elastic structure where a…
In this paper is discussed a class of static spherically symmetric solutions of the general relativistic elasticity equations. The main point of discussion is the comparison of two matter models given in terms of their stored energy…
The uniaxial elastic-plastic deformation process is considered. Mathematical model of this process was built. According to this model all stable static states form the lattice, which is called the delta-lattice.