Conformal elasticity of mechanism-based metamaterials

Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate symmetry due to the presence of a designer soft strain pathway. Here we show that low energy deformations of designer dilational metamaterials will be governed by a scalar field theory, conformal elasticity, in which the nonuniform, nonlinear deformations observed under generic loads correspond with the well-studied—conformal—maps. We validate this approach using experiments and finite element simulations and further show that such systems obey a holographic bulk-boundary principle, which enables an analytic method to predict and control nonuniform, nonlinear deformations. This work both presents a unique method of precise deformation control and demonstrates a general principle in which mechanisms can generate special classes of soft deformations.

Nonlinear deformations of a cylindrical pipe with pre-stressed thin coatings

The paper presents an exact solution for the problem of large deformations of torsion, axial tension–compression, and radial expansion or shrinkage of an elastic hollow circular cylinder equipped with pre-stressed elastic coatings. Surface coatings are modeled using the six-parameter nonlinear shell theory. The constitutive material of the cylinder is described by a three-dimensional nonlinear model of the isotropic incompressible body of the general form. Special boundary conditions describe the interaction of this material with thin coatings on the inner and outer surface of the pipe. Based on the solution obtained, numerical calculations were performed on the effect of preliminary stresses in coatings on the stress–strain state of a cylindrical pipe.

A science friction story – Molecular interactions in semiflexible polymer networks

Established model theories, developed to capture the mechanical behavior of soft complex materials composed of semiflexible polymers assume entropic interactions between filaments to determine the mechanical response. In recent studies, the general accepted tube model has been challenged in terms of its basic assumption about filament-filament interactions, but also because of its predictions regarding the frequency dependence of the elastic modulus in the intermediate frequency regime. A central question is how molecular interactions and friction between network constituents influence the rheological response of isotropic entangled networks of semiflexible polymers. It was shown that friction forces between aligned pairs of actin filaments are not negligible. Here, we systematically investigate the influence of friction forces and attractive interactions on network rheology by means of a targeted surface modification. We show that these forces have a qualitative and quantitative influence on the viscoelastic properties of semiflexible polymer networks and contribute to the response to nonlinear deformations. By comparing two polymer model systems with respect to their surface compositions we give a possible explanation about the origin of acting forces on a molecular level.

Flexible Mass Spring Method for Modelling Soft Tissue Deformation

It is well accepted that soft tissue deformation is a combination of linear and nonlinear response. During small displacements, soft tissues deform linearly while during large displacements, soft tissues show nonlinear deformation. This paper presents a new approach for modelling of soft tissue deformation, from the standpoint of Mass Spring Method (MSM). The proposed MSM model is developed using conical spring methodology which allow the MSM model to have different stiffnesses at different displacements during deformation. The stiffness variation creates flexibility in the model to simulate any linear and nonlinear deformations. Experimental results demonstrate that the deformations by the proposed method are in good agreement with those real and phantom soft tissue deformations. Isotropic and anisotropic deformations can be accommodated by the proposed methodology via conical spring geometry and configuration of the springs. The proposed model also able to simulate typical viscoelastic behaviour of soft tissue.

Mechanics of two filaments in tight orthogonal contact

Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear deformations, and friction. Here, we perform an in-depth study of a simple, yet canonical, problem that captures the essence of contact between filaments. In the orthogonal clasp, two filaments are brought into contact, with each centerline lying in one of a pair of orthogonal planes. Our data from X-ray tomography (μCT) and mechanical testing experiments are in excellent agreement with finite element method (FEM) simulations. Despite the apparent simplicity of the physical system, the data exhibit strikingly unintuitive behavior, even when the contact is frictionless. Specifically, we observe a curvilinear diamond-shaped ridge in the contact-pressure field between the two filaments, sometimes with an inner gap. When a relative displacement is imposed between the filaments, friction is activated, and a highly asymmetric pressure field develops. These findings contrast to the classic capstan analysis of a single filament wrapped around a rigid body. Both the μCT and FEM data indicate that the cross-sections of the filaments can deform significantly. Nonetheless, an idealized geometrical theory assuming undeformable tube cross-sections and neglecting elasticity rationalizes our observations qualitatively and highlights the central role of the small, but nonzero, tube radius of the filaments. We believe that our orthogonal clasp analysis provides a building block for future modeling efforts in frictional contact mechanics of more complex filamentary structures.

Influence of Rotational Stiffness Modeling on the Joint Behavior of Quasi-Rectangular Shield Tunnel Linings

A beam-spring model with constant rotational stiffness is a practical tool for the prediction of the general deformations and bending moments in circular tunnel linings. However, in reality, the rotational stiffness of a segmental joint is not constant, due to nonlinear deformations and local yielding in the vicinity of the joint. These are a result of the specific geometry at the joint, which is related to water-tightness measures and buildability issues. For quasi-rectangular tunnels this nonlinearity should not be neglected, as the bending component in the lining is significantly larger compared to circular linings. To date, there are only few studies that have investigated a calculation method for consideration of the joint’s nonlinear moment-axial force and shear-axial force interaction behavior and its consequences on the calculated lining behavior. In this paper, an iterative incremental method is proposed to tackle this issue, based on rotational stiffness curves derived from 3D nonlinear finite element modelling of the joints, and substantiated by testing. The significance of the variable rotational stiffness is highlighted through a comparison with results based on a constant stiffness assumption. Further, using the proposed calculation method, the effects of the circumferential joints, the bending moment transmission and several other parameters on the full-ring behavior of quasi-rectangular tunnels are discussed for a wide interval of design parameters. The results provide some new insights into the behavior of this non-traditional tunnel type. Although the presented results are related to specific overall and local geometries, the presented method is considered to be useful for the design of other special tunnel geometries.

Magnetic deformation of super-Maxwell theory in supergravity

A necessary condition for partial breaking of $$ \mathcal{N} $$ N = 2 global supersymmetry is the presence of nonlinear deformations of the field transformations which cannot be generated by background values of auxiliary fields. This work studies the simplest of these deformations which already occurs in $$ \mathcal{N} $$ N = 1 global supersymmetry, and its coupling to supergravity. It can be viewed as an imaginary constant shift of the D-auxiliary real field of an abelian gauge multiplet. We show how this deformation describes the magnetic dual of a Fayet-Iliopoulos term, a result that remains valid in supergravity, using its new-minimal formulation. Local supersymmetry and the deformation induce a positive cosmological constant. Moreover, the deformed U(1) Maxwell theory coupled to supergravity describes upon elimination of the auxiliary fields the gauging of R-symmetry, realised by the Freedman model of 1976. To this end, we construct the chiral spinor multiplet in superconformal tensor calculus by working out explicitly its transformation rules and use it for an alternative description of the new-minimal supergravity coupled to a U(1) multiplet. We also discuss the deformed Maxwell theory in curved superspace.

DEPENDENCE OF GLARE DESTRUCTION MECHANISMS ON THE ELONGATION OF SAMPLES IN TESTS TO THREE-POINT FLEXURAL

Tests on bending are one of the effective ways to experimentally determine the elasticity and shear moduli. An important task in the implementation of composite materials in aerospace structures is the development of methods for determining the physical and mechanical characteristics of materials. The paper presents of tests for three-point bending of samples of metal-polymer composite material "GLAss-REinforced" Fibre Metal Laminate (GLARE) are presented. Examined samples, consisting of 17 layers, for which apparent interlayer strength of the results of tests on three-point bending was established by the method of "short beam". It was established that for the studied samples, interlayer shear mechanisms were realized at the ratio of dimensions of length to thickness of at least 10. Localization of fracture occurs in the area of the central layer, which corresponds to the requirements of standards for conducting tests of the method of short beams. Nonetheless, such GLARE tests are always accompanied by the occurrence of significant plastic deformations associated with the presence of aluminum layers in the structure of the material. With the elongation of samples of more than 10, a fracture mechanism is realized in them, during which delamination and loss of stability of the outer layers on the compressed side of the sample occur. When the elongation of samples of less than 4 four is implemented in samples takes place, the mechanism of destruction of indentation type with large nonlinear deformations. According to the test results, the dependence of the realised fracture mechanisms on the elongation of the samples is determined.

InSAR techniques to determine mining-related deformations using Sentinel-1 data: the case study of Rydułtowy mine in Poland.

<p>Since launching Sentinel 1 satellites, the European Space Agency has been providing a huge amount of repeated SAR data. Thanks to 6-days revisiting time, it creates a perfect possibility for the monitoring of ground deformation, caused by underground mining activity, by using Differential SAR interferometry (DInSAR).</p><p>Because, DInSAR exploits single interferometric SAR pairs, the accuracy of this technique is limited by spatial and temporal decorrelation and atmospheric artifacts. To minimize the atmospheric influence on DInSAR results, we investigated precipitation and relative humidity data acquired from the Institute of Meteorology and Water Management (IMGW). Theoretically, the summed atmospheric LOS errors due to relative humidity for 106 ascending and 112 descending images are -3.5 cm and 7,5 cm, respectively.  In fact, we observed that there is a moderate correlation between precipitation/relative humidity and “bad” acquisition in relatively small study area. Nevertheless, we were able to remove 33 ascending and 15 descending images from the queue of consecutive DInSAR. Finally, it allowed to estimate up to 1m subsidence in the period of 1 Jan 2017–8 Oct 2018 in the Rydułtowy mine located in the southwest part of the Upper Silesian Coal Basin (USCB), Poland.</p><p>To evaluate our DInSAR accuracy due to atmospheric artefacts, we decided to compare the results with “atmospheric-free” results acquired by SBAS technique. SBAS separates diverse interferometric components that correspond to deformation, topographic error, atmospheric error, and orbital errors.</p><p>The Root-Mean-Square Error (RMSE) has been calculated between SBAS and DInSAR for selected subsidence profiles. The maximal RMSE was found to be 3.6 cm and 4.1cm for ascending and descending LOS displacements, respectively. This shows that DInSAR cannot be used for monitoring millimeter-level deformation. On the contrary, it can be effectively used to assess quick nonlinear deformations reaching several decimeters /year such as in the presented study case.</p>