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The modern theory of elasticity and the first law of thermodynamics are cornerstones of engineering science that share the concept of reversibility. Engineering researchers have known for four decades that the modern theory violates the…
Lattice structures have been widely used in various applications of additive manufacturing due to its superior physical properties. If modeled by triangular meshes, a lattice structure with huge number of struts would consume massive…
We shall consider some common models in linear thermo-elasticity within a common structural framework. Due to the flexibility of the structural perspective we will obtain well-posedness results for a large class of generalized models…
Dynamics of the 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 expression…
The ``Eshelby problem" refers to the response of a 2-dimensional elastic sheet to cutting away a circle, deforming it into an ellipse, and pushing it back. The resulting response is dominated by the so-called ``Eshelby Kernel" which was…
Recent developments in the engineering of metamaterials have brought forth a myriad of mesmerizing mechanical properties that do not exist in ordinary solids. Among these, twisting metamaterials, acoustical chirality, or Willis coupling are…
Anelasticity, as an intrinsic property of amorphous solids, plays a significant role in understanding their relaxation and deformation mechanism. However, due to the lack of long-range order in amorphous solids, the structural origin of…
A four-parameter kinematic model for the position of a fluid parcel in a time-varying ellipse is introduced. For any ellipse advected by an arbitrary linear two-dimensional flow, the rates of change of the ellipse parameters are uniquely…
We examine here various aspects of the statics and dynamics of disordered elastic systems such as manifolds and periodic systems. Although these objects look very similar and indeed share some underlying physics, periodic systems constitute…
We report the counter-intuitive instability of charged elastic rings, and the persistence of sinusoidal deformations in the lowest-energy configurations by the combination of high-precision numerical simulations and analytical perturbation…
We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions. Our approach encompasses both sleeve and adhesion problems, and provides simple and…
We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…
In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination…
Wrinkling instabilities of thin elastic sheets can be used to generate periodic structures over a wide range of length scales. Viscosity of the thin elastic sheet or its surrounding medium has been shown to be responsible for dynamic…
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…
Fractal is an intriguing geometry with self-similarity and non-integer dimensions, the elastic-wave topological phase based on fractal structures has not been revealed up to now. In this work, elastic-wave higher-order topological states in…
We investigate the motions of a bar structure consisting of two congruent tetrahedra, whose edges in their basic position form the face diagonals of a rectangular parallelepiped. The constraint of the motion is that the originally…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…
By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with…