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Several experiments have demonstrated the existence of an electro-mechanical effect in many biological tissues and hydrogels, and its actual influence on growth, migration, and pattern formation. Here, to model these interactions and…
Many studies investigated the application of statistical mechanics to damage phenomena. However, so far the association of damage with statistical mechanics is far from completely developed. One of the most successful approaches maps the…
Elastic geodesic grids (EGG) are lightweight structures that can be easily deployed to approximate designer provided free-form surfaces. In the initial configuration the grids are perfectly flat, during deployment, though, curvature is…
Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity. In this work, we report on the description of continuous elastic fields derived…
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…
The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes,…
We present a novel derivation of the elastic theory of shells. We use the language of Geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools…
Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden non-spatial symmetries can occur…
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…
The surface reconstruction problem from sets of planar parallel slices representing cross sections through 3D objects is presented. The final result of surface reconstruction is always based on the correct estimation of the structure of the…
The constitutive characterization of the uniformity and homogeneity of binary elastic composites is presented in terms of a combination of the material groupoids of the individual constituents. The incorporation of these two groupoids…
A geometrical interpretation of the $G$-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of…
By the simple finite element method, we study the symplectic, multisymplectic structures and relevant preserving properties in some semi-linear elliptic boundary value problem in one-dimensional and two-dimensional spaces respectively. We…
Chromonic liquid crystals (CLCs) are lyotropic materials which are attracting growing interest for their adaptability to living systems. A considerable body of works has been devoted to exploring their properties and applications. In this…
In this paper, we discuss the dynamic modeling of fluid-filled straw-like elements consisting of serially interconnected elastic frusta with both axisymmetric and antisymmetric degrees of freedom, assuming planar motion. Under appropriate…
Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.
Many elastic structures exhibit rapid shape transitions between two possible equilibrium states: umbrellas become inverted in strong wind and hopper popper toys jump when turned inside-out. This snap-through is a general motif for the…
Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…
Architected materials achieve unique mechanical properties through precisely engineered microstructures that minimize material usage. However, a key challenge of low-density materials is balancing high stiffness with stable deformability up…
Materials in which electrons occupy interstitial sites as anions are called electrides and exhibit unusual dimensionality-dependent electronic behavior. These properties make electrides attractive for catalysis, transparent conductors, and…