相关论文: Fractal space frames and metamaterials for high me…
Because of Euler buckling, a simple strut of length $L$ and Young modulus $Y$ requires a volume of material proportional to $L^3 f^{1/2}$ in order to support a compressive force $F$, where $f=F/YL^2$ and $f\ll 1$. By taking into account…
The principle of hierarchical design is a prominent theme in many natural systems where mechanical efficiency is of importance. Here we establish the properties of a particular hierarchical structure, showing that high mechanical efficiency…
We consider a plate made from an isotropic but brittle elastic material, which is used to span a rigid aperture, across which a small pressure difference is applied. The problem we address is to find the structure which uses the least…
In many scenarios -- when we bite food or during a crash -- fracture is inevitable. Finding solutions to steer fracture to mitigate its impact or turn it into a purposeful functionality, is therefore crucial. Strategies using composites,…
Fractal patterns are observed in computational mechanics of elastic-plastic transitions in two models of linear elastic/perfectly-plastic random heterogeneous materials: (1) a composite made of locally isotropic grains with weak random…
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…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
Accurately predicting when and how materials fail is critical to designing safe, reliable structures, mechanical systems, and engineered components that operate under stress. Yet, fracture behavior remains difficult to model across the…
Fractons are exotic quasiparticles whose mobility in space is restricted by symmetries. In potential real-world realisations, fractons are likely lodged to a physical material rather than absolute space. Motivated by this, we propose and…
Material strength is a classical concept with renewed importance in fracture mechanics, particularly in crack nucleation in brittle solids. We formulate material strength in finite elasticity and examine its geometric, constitutive, and…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
The fractal cosmological model which accounts for observable fractal properties of the Universe's large-scale structure is constructed. In this framework these properties are consequences of the rotary symmetry of charged scalar meson…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
While numerous examples of fractal spaces may be found in various fields of science, the flow of time is typically assumed to be one-dimensional and smooth. Here we present a metamaterial-based physical system, which can be described by…
We investigate the geometrically nonlinear deformation and buckling of a slender elastic beam subject to time-dependent `fictitious' (non-inertial) forces arising from unsteady rotation. Using a rotary apparatus that accurately imposes an…
This paper proposes a methodology for architecting microstructures with extremal stiffness, yield, and buckling strength using topology optimization. The optimized microstructures reveal an interesting transition from simple lattice like…
The Young's modulus of a two-dimensional truss-like structure is simulated by using the finite element method. A power-law expression is proposed for the effective Young's modulus of the system. The obtained numerical results are compared…
Jammed packings of granular materials display complex mechanical response. For example, the ensemble-averaged shear modulus $\left\langle G \right\rangle$ increases as a power-law in pressure $p$ for static packings of soft spherical…
Bone adapts in response to its mechanical environment. This evolution of bone density is one of the most important mechanisms for developing fracture resistance. A finite element framework for simulating bone adaptation, commonly called…
We describe the out-of-plane bending of chiral fractal lattices metamaterials by using a combination of theoretical models, full-scale finite elements and experimental tests representing the flexural behaviour of metamaterial beams under…