Negative Stiffness, Incompressibility and Strain Localisation in Particulate Materials

In this paper, we consider two mechanisms capable of inducing strain localisation in particulate geomaterials in compression: the apparent negative stiffness and the incremental incompressibility caused by dilatancy. It is demonstrated that the apparent negative stiffness can be produced by the rotation of clusters of particles in the presence of compression. The clusters are formed by connecting the particles by the bonds that still remain intact in the process of bond breakage in compression. We developed a 2D isotropic model of incremental incompressibility showing that a single strain localisation zone is formed inclined at 45° to the direction of axial compressive loading. This mechanism of localisation was analysed through Particle Flow Code (PFC) 2D and 3D simulations. It is shown that, in the simulations, the peak stress (the onset of localisation) does correspond to the incremental Poisson’s ratio, reaching the critical values of 1 (in 2D) and 0.5 (in 3D).

Investigation of deformation behavior of PETG-FDM-printed metamaterials with pantographic substructures based on different slicing strategies

Based on the progress and advances of additive manufacturing technologies, design and production of complex structures became cheaper and therefore rather possible in the recent past. A promising example of such complex structure is a so-called pantographic structure, which can be described as a metamaterial consisting of repeated substructure. In this substructure, two planes, which consist of two arrays of beams being orthogonally aligned to each other, are interconnected by cylinders/pivots. Different inner geometries were taken into account and additively manufactured by means of fused deposition modeling technique using polyethylene terephthalate glycol (PETG) as filament material. To further understand the effect of different manufacturing parameters on the mechanical deformation behavior, three types of specimens have been investigated by means of displacement-controlled extension tests. Different slicing approaches were implemented to eliminate process-related problems. Small and large deformations are investigated separately. Furthermore, 2D digital image correlation was used to calculate strains on the outer surface of the metamaterial. Two finite-element simulations based on linear elastic isotropic model and linear elastic transverse isotropic model have been carried out for small deformations. Standardized extension tests have been performed on 3D-printed PETG according to ISO 527-2. Results obtained from finite-element method have been validated by experimental results of small deformations. These results are in good agreement with linear elastic transverse isotropic model (up to about [Formula: see text] of axial elongation), though the response of large deformations indicates a nonlinear inelastic material behavior. Nevertheless, all samples are able to withstand outer loading conditions after the first rupture, resulting in resilience against ultimate failure.

О разрушении упругих полимерных материалов под воздействием электронного пучка

An explanation for a feature found in several experiments in the general picture of the destruction of non-brittle polymers under the influence of a shock wave initiated by a powerful electron beam is proposed. The distance of the cracking region from the surface of the material affected by the beam to a finite length in depth is associated with the three-dimensional nature of the propagation of elastic waves. The universality of the effect is demonstrated by the simplest isotropic model, which shows that large tensile stresses are effectively generated inside the target at its sufficiently large transverse and longitudinal size, even without taking into account nonlinear and shear processes.

Are stellar-mass binary black hole mergers isotropically distributed?

ABSTRACT The Advanced LIGO and Advanced Virgo gravitational wave detectors have detected a population of binary black hole mergers in their first two observing runs. For each of these events, we have been able to associate a potential sky location region represented as a probability distribution on the sky. Thus, at this point we may begin to ask the question of whether this distribution agrees with the isotropic model of the Universe, or if there is any evidence of anisotropy. We perform Bayesian model selection between an isotropic and a simple anisotropic model, taking into account the anisotropic selection function caused by the underlying antenna patterns and sensitivity of the interferometers over the sidereal day. We find an inconclusive Bayes factor of 1.3: 1, suggesting that the data from the first two observing runs are insufficient to pick a preferred model. However, the first detections were mostly poorly localized in the sky (before the Advanced Virgo joined the network), spanning large portions of the sky and hampering detection of potential anisotropy. It will be appropriate to repeat this analysis with events from the recent third LIGO observational run and a more sophisticated cosmological model.

INFLUENCE OF STRUCTURAL DEFECTS ON NONEQUILIBRIUM CRITICAL BEHAVIOR OF THREE-DIMENSIONAL ANISOTROPIC HEISENBERG MODEL

The results of a Monte Carlo study of features of structural defects influence on nonequi-librium critical behavior of three-dimensional isotropic and anisotropic Heisenberg models are presented with their evolution from different initial states. It is shown that presence of defects changes characteristics of nonequilibrium critical behavior of anisotropic model with easy axis anisotropy type and evolution from both high-temperature and low-temperature initial states. Presence defects is relevant only for characteristics of nonequi-librium critical behavior of isotropic model with evolution from low-temperature initial state leading to superaging effects.

Amplitude signatures in fractured media

<p>Most of existing rocks are typically fractured that effectively result in anisotropic model of different complexity (Tsvankin and Grechka, 2011). The anisotropy signatures can be defined by traveltime and reflection&transmission amplitudes at plane interface between the rocks of different properties. Here, we focus on reflection amplitude by introducing the uniform approach to embed the fracture sets of different orientation. We utilize the linear slip theory (Schoenberg and Helbig, 1997) to add the fractures of arbitrary weakness parameters. The anisotropic model sequence consists of isotropic model (later used as a background), transversely isotropic model with a vertical symmetry axis (due to horizontal fracture set), orthorhombic model (due to horizontal and vertical fracture sets), monoclinic model with a horizontal symmetry plane (due to horizontal and two non-orthogonal vertical fracture sets) and triclinic model (due to horizontal, two non-orthogonal vertical and one inclined fracture sets). The general equation for the matrix of stiffness coefficients is given by the inverse sum of the fracture weakness matrices multiplied with density. The isotropic background stiffness coefficient matrix is defined by inverse of background weakness matrix. Each fracture weakness matrix generally has three independent parameters that are normal, tangential and horizontal weaknesses. In addition to these parameters, the fracture orientation angles in 3D space are also taken into account, and the rotation matrix is defined for each set of fractures. The uniform non-rotated weakness matrix can be chosen for brevity’s sake, however, all fracture sets might have their own weaknesses. We analyze the plane P wave reflection coefficient computed at plane interface between isotropic background and fractured background half-spaces. It is convenient to show reflection coefficient versus horizontal slowness projections. To compute reflection coefficients, we use the method developed by Jin and Stovas (2020).</p><p>The fracture sets of different orientation affect azimuthally dependent amplitude signatures. By using proposed method, the fracture set parameters and orientation can be estimated from seismic data.</p><p><strong>References</strong></p><p>Tsvankin, I., and V. Grechka, 2011, Seismology of azimuthally anisotropic media and seismic fracture characterization. SEG.</p><p>Schoenberg, M., and K. Helbig, 1997, Orthorhombic media: Modeling elastic wave behavior in avertically fractured earth. Geophysics, <strong>62</strong>(2). 1954-1974.</p><p>Jin, S., and A. Stovas, 2020, Reflection and transmission approximations for monoclinic media with a horizontal symmetry plane. Geophysics (early view).</p>