On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions

The problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated and studied. It is proved a theorem of existence and uniqueness of a weak solution for the problem under consideration.

Soft-lubrication interactions between a rigid sphere and an elastic wall

The motion of an object within a viscous fluid and in the vicinity of a soft surface induces a hydrodynamic stress field that deforms the latter, thus modifying the boundary conditions of the flow. This results in elastohydrodynamic interactions experienced by the particle. Here, we derive a soft-lubrication model, in order to compute all the forces and torque applied on a rigid sphere that is free to translate and rotate near an elastic wall. We focus on the limit of small deformations of the surface with respect to the fluid-gap thickness, and perform a perturbation analysis in dimensionless compliance. The response is computed in the framework of linear elasticity, for planar elastic substrates in the limiting cases of thick and thin layers. The EHD forces are also obtained analytically using the Lorentz reciprocal theorem.

Line strain representation and shear strain representation of 3D strain states

The strain state in 3D space is usually expressed by the conventional method of combining three linear and shear strains. Due to the obvious differences between the first two strains, it is necessary to uncover their properties when describing deformation, studying yield and failure, and developing test apparatus or equipment. The difficulties encountered in the above work would be greatly simplified if strain states could be expressed in a single strain form, namely including only linear or shear strains. As a start, this paper explores the meaning and nature of strain states. Then, based on the hypothesis of small deformations, two strain state expressions, the linear strain expression method (LSEM) and shear strain expression method (SSEM), were established for incompressible materials with only linear strain and shear strain as parameters respectively. Furthermore, conditions, implementation steps and specific forms for the application of SSEM in 1D, 2D and 3D strain states are obtained. As an example, two representations based on tetragonal pyramid and rotating tetrahedron are especially given. Therefore, conventional strain representation methods can be expressed as a combination of line strains in a certain direction or a combination of characteristic shear strains. The results of this paper provide a new way for understanding deformation characteristics, revealing yielding process, establishing constitutive models, and developing testing apparatus or equipment.

Obstruction flat rigidity of the CR 3-sphere

We consider the obstruction flatness problem for small deformations of the standard CR 3-sphere. That rigidity holds for the CR sphere was previously known (in all dimensions) for the case of embeddable CR structures, where it also holds at the infinitesimal level. In the 3-dimensional case, however, a CR structure need not be embeddable. Unlike in the embeddable case, it turns out that in the nonembeddable case there is an infinite-dimensional space of solutions to the linearized obstruction flatness equation on the standard CR 3-sphere and this space defines a natural complement to the tangent space of the embeddable deformations. In spite of this, we show that the CR 3-sphere does not admit nontrivial obstruction flat deformations, embeddable or nonembeddable.

Deformations of higher-page analogues of $$\partial {{\bar{\partial }}}$$-manifolds

We extend the notion of small essential deformations of Calabi–Yau complex structures from the case of the Iwasawa manifold, for which they were introduced recently by the first-named author, to the general case of page-1-$$\partial {{\bar{\partial }}}$$ ∂ ∂ ¯ -manifolds that were jointly introduced very recently by all three authors. We go on to obtain an analogue of the unobstructedness theorem of Bogomolov, Tian and Todorov for Calabi–Yau page-1-$$\partial {{\bar{\partial }}}$$ ∂ ∂ ¯ -manifolds. As applications of this discussion, we study the small deformations of certain Nakamura solvmanifolds and reinterpret the cases of the Iwasawa manifold and its 5-dimensional analogue from this standpoint.

Two dimensional V2O3 and its experimental feasibility as robust room-temperature magnetic Chern insulator

The possibility of dissipationless chiral edge states without the need of an external magnetic field in the quantum anomalous Hall effect (QAHE) offers a great potential in electronic/spintronic applications. The biggest hurdle for the realization of a room-temperature magnetic Chern insulator is to find a structurally stable material with a sufficiently large energy gap and Curie temperature that can be easily implemented in electronic devices. This work based on first-principle methods shows that a single atomic layer of V2O3 with honeycomb–kagome (HK) lattice is structurally stable with a spin-polarized Dirac cone which gives rise to a room-temperature QAHE by the existence of an atomic on-site spin–orbit coupling (SOC). Moreover, by a strain and substrate study, it was found that the quantum anomalous Hall system is robust against small deformations and can be supported by a graphene substrate.

A Comparison of Biomechanical Properties of Implant-Retained Overdenture Based on Precision Attachment Type

This paper aims to compare, in vitro, the biomechanical properties of an overdenture retained by two bar-retained implants and an overdenture retained by two bar-retained implants with ball attachments. An edentulous mandible model was prepared for the study based on the FRASACO mold with two implants. In the first system, the “rider” type (PRECI-HORIX, CEKA) retention structure and the complete mandibular denture with the matrix were made. In the second system, the “rider” type retention suprastructure was also used. In the distal part, (CEKA) clips were placed symmetrically, and a complete mandibular denture, together with the matrix on the bar, and the clip patrices were made. A numerical model was developed for each system where all elements were positioned and related to geometric relations, as in reality. The FEA analysis (finite element analysis) was carried out for seven types of loads: with vertical forces of 20, 50, and 100 N and oblique forces of 20 and 50 N acting on individual teeth of the denture, namely central incisor, canine, and first molar. Displacements, stresses, and deformations within the systems were investigated. Maximum denture displacement in the first system was 0.7 mm. Maximum bar stress amounted to 27.528 MPa, and implant stress to 23.16 MPa. Maximum denture displacement in the second system was 0.6 mm. Maximum bar stress amounted to 578.6 MPa, that of clips was 136.99 MPa, and that of implants was 51.418 MPa. Clips cause smaller displacement of the overdenture when it is loaded but generate higher stress within the precision elements and implants compared to a denture retained only by a bar. Regardless of the shape of the precision element, small deformations occur that mainly affect the mucosa and the matrix.

A note on viscoelastic bodies whose material properties depend on the density

In this note, we study the response of a viscoelastic body whose stress relaxation modulus and creep compliance depend on the density of the body in such a manner that the stress and strain appear linearly in the constitutive equation. Such models would be useful to study the response of porous viscoelastic bodies undergoing small deformations, as the moduli depend on the porosity, and hence the density. We study the problem of tension–torsion of cylinders of arbitrary cross-section within the context of this constitutive relation.

Giant gauge factor of Van der Waals material based strain sensors

There is an emergent demand for high-flexibility, high-sensitivity and low-power strain gauges capable of sensing small deformations and vibrations in extreme conditions. Enhancing the gauge factor remains one of the greatest challenges for strain sensors. This is typically limited to below 300 and set when the sensor is fabricated. We report a strategy to tune and enhance the gauge factor of strain sensors based on Van der Waals materials by tuning the carrier mobility and concentration through an interplay of piezoelectric and photoelectric effects. For a SnS2 sensor we report a gauge factor up to 3933, and the ability to tune it over a large range, from 23 to 3933. Results from SnS2, GaSe, GeSe, monolayer WSe2, and monolayer MoSe2 sensors suggest that this is a universal phenomenon for Van der Waals semiconductors. We also provide proof of concept demonstrations by detecting vibrations caused by sound and capturing body movements.