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Recent discoveries in differential topology are reviewed in light of their possible implications for spacetime models and related subjects in theoretical physics. Although not often noted, a particular smoothness (differentiability)…
Anisotropy, as an exotic degree of freedom, enables us to discover the emergent two-dimensional (2D) layered nanomaterials with low in-plane symmetry and to explore their outstanding properties and promising applications. 2D black arsenic…
We introduce a computational method and a user-friendly code with a terminal-based graphical user interface (GUI), named ElATools, developed to analyze mechanical and anisotropic elastic properties. ElATools enables facile analysis of the…
This paper investigates the effects of plasticity on the effective fracture toughness. A layered material is considered as a modelling system. An elastic-plastic phase-field model and a surfing boundary condition are used to study how the…
Anisotropies of Young's modulus E, the shear modulus G, and Poisson's ratio of all 2D symmetry systems are studied. Simple necessary and sufficient conditions on their elastic compliances are derived to identify if any of these crystals are…
Heterogeneous materials exhibit anisotropy which is influenced by factors such as individual phase properties and microstructural configuration that form crucial descriptors of heterogeneity. A review of anisotropy indices proposed in the…
Odd transport phenomena -- defined as a flux response orthogonal to an applied gradient -- have been recently observed in isotropic systems, with a multitude of proposed models and experiments to study these effects. Odd transport manifests…
Several families of elastic anisotropies were introduced by Saint Venant (1863) for which the polar diagram of elastic parameters in different directions of the material (indicator surface) are ellipsoidal. These families recover a large…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…
We develop the theory of anomalous elasticity in two-dimensional flexible materials with orthorhombic crystal symmetry. Remarkably, in the universal region, where characteristic length scales are larger than the rather small Ginzburg scale…
Layered materials span a very broad range of solids ranging from van der Waals materials to highly complex crystal structures such as clays. They are commonly believed to have highly anisotropic properties, which is essentially attributed…
Term "asymmetrical pseudoelasticity" refers to the theory, in which a symmetrical stress tensor and a symmetrical strain tensor are connected by means of an asymmetrical material tensor. An 6-dimensional asymmetrical matrix of elasticity…
3D-printed digital materials whose mechanical behavior travels between those from thermoplastic to rubbery polymers have become increasingly important. However, their mechanical functionalities have not been fully exploited due to intrinsic…
Hooke's law states that the forces or stresses experienced by an elastic object are proportional to the applied deformations or strains. The number of coefficients of proportionality between stress and strain, i.e., the elastic moduli, is…
The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…
In this work, we derive a three-dimensional effective mass that is suitable for treatment of electrons in anisotropic semiconductors. We show that it is possible to define a scalar anisotropic three-dimensional mass that reduces to a…
The essential role played by differentiable structures in physics is reviewed in light of recent mathematical discoveries that topologically trivial space-time models, especially the simplest one, ${\bf R^4}$, possess a rich multiplicity of…
Chiral active materials are abundant in nature, including the cytoskeleton with attached motor proteins, rotary clusters of bacteria flagella, and self-spinning starfish embryos. These materials break both time reversal and mirror-image…
Customarily, in-plane auxeticity and synclastic bending behavior (i.e. out-of-plane auxeticity) are not independent, being the latter a manifestation of the former. Basically, this is a feature of three-dimensional bodies. At variance,…
Uniaxial elastomers are characterized by five elastic constants. If their elastic modulus C_5 describing the energy of shear strains in planes containing the anisotropy axis vanishes, they are said to be soft. In spatial dimensions d less…