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A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
In structural rigidity, one studies frameworks of bars and joints in Euclidean space. Such a framework is an articulated structure consisting of rigid bars, joined together at joints around which the bars may rotate. In this paper, we will…
The elasticity difference tensor, used in [1] to describe elasticity properties of a continuous medium filling a space-time, is here analysed from the point of view of the space-time connection. Principal directions associated with this…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
Abstract. We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points,…
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is…
The atomic structure and elastic properties of silicon carbide nanowires of different shapes and effective sizes were studied using density functional theory and classical molecular dynamics. The surface relaxation led to surface…
In classical geometry, there is no such well-known and much-studied topic as the construction of conic sections (or briefly conics) from its five points. Its importance in many applications of mechanical engineering, civil engineering and…
For solving the longstanding materials science problem of correlating elastic properties of a solid material to the formation of cracks we present a new general concept. This concept is applied to the technologically most important cracks…
The aim of this paper is to extend basic understanding of Engel structures through developing geometric constructions which are canonical to a certain degree and the dynamics of Cauchy characteristics in the transverse spaces which may…
This is a paper about triangle cubics and conics in classical geometry with elements of projective geometry. In recent years, N.J. Wildberger has actively dealt with this topic using an algebraic perspective. Triangle conics were also…
Surface roughness emerges naturally during mechanical removal of material, fracture, chemical deposition, plastic deformation, indentation, and other processes. Here, we use continuum simulations to show how roughness which is neither…
This paper deals with a concept for a reconfigurable structure bio-inspired by the cell wall architecture of euglenids, a family of unicellular protists, and based on the relative sliding of adjacent strips. Uniform sliding turns a cylinder…
Macroscopic elastic core-shell systems can be generated as toy models to be deformed and haptically studied by hand. On the mesoscale, colloidal core-shell particles and microgels are fabricated and investigated by different types of…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The…
We consider in a simple and general way elastic waves in isotropic and anisotropic media, their polarization, speeds, reflection from interfaces with mode conversion, and surface waves. Reflection of quasi transverse waves in anisotropic…
The initial techniques developed in Euclid's Elements, well before the use of the parallel postulate, are reexamined in order to clarify even the most obscure details, particularly those related to equality, superposition and angle…
There have been some interesting recent advances in understanding the notion of mechanical disorder in structural glasses and the statistical mechanics of these systems' low-energy excitations. Here we contribute to these advances by…