Numerical simulation of slow deformation perturbations in fault zones

Over the past half a century, the concept of slow deformation waves of the Earth has been developed and widely discussed in the Earth sciences. The velocity of slow waves is considered to be 5–6 orders of magnitude less than the velocity of sound and 7–8 orders of magnitude greater than tectonic flows. Analyzing and classifying various manifestations of slow deformation waves in the geomedium accumulated over forty years V. G. Bykov identifies two types of autowaves in his review—inter-fault and intra-fault. Here, the process of generation and propagation of slow deformation disturbances between two faults in an elastoplastic medium is studied numerically. The faults were defined as narrow elongated soft areas inclined to the axis of the load application. Just in these faults plastic deformation was permitted to generate. The simulations proved that the fronts of deformation waves head towards each other at approximately the same velocities, their shapes being close to planar but slightly curved

Numerical analysis of the stress state and fracture of porous ceramics at the mesolevel

The paper is devoted to the numerical investigation of inelastic deformation and fracture of porous alumina ceramics. A structural model of the mesovolume is developed with the use of an experimental scanning electron microscopic image. The mechanical behavior of the matrix is described by two constitutive models from plasticity theory and continuum damage mechanics. Uniaxial tension and compression of the mesovolume are numerically simulated in a two-dimensional formulation. The features of fracture patterns in the cases of the two constitutive models adopted are analysed. Effective mechanical characteristics of the studied ceramics are determined from the performed calculations. The results obtained can be used to specify the characteristics of the Drucker–Prager material for macroscopic modeling

Study of effect of damage accumulation on stress distribution parameters in mesovolume of biocomposite and its performance characteristics

Abstract—A numerical study of mechanical properties of zirconium ceramic–cortical bone tissue biocomposite has been fulfilled using a multiple-scale approach. Evolution of mesoscopic stress distribution in the components of biocomposite during its deformation has been studied with the assumption of damage accumulation until the macrostrength criterion is fulfilled. It has been shown that the parameters of the laws of distribution change with damage accumulation

Numerical investigation of effective mechanical properties of metal-ceramic composites with reinforcing inclusions of different shapes under intensive dynamic impacts

In the present paper, the results of numerical simulation of high-rate deformation of stochastic metal-ceramic composite materials Al–50% B4C, Al–50% SiC, and Al–50% Al2O3 at the mesoscopic scale level under loading by a plane shock wave are presented. Deformation of the mesoscopic volume of a composite, whose structure consists of the aluminum matrix and randomly distributed reinforcing ceramic inclusions, is numerically simulated. The results of the numerical simulation are used for the investigation of special features of the mechanical behavior at the mesoscopic scale level under shock-wave loading and for the numerical evaluation of effective elastic and strength properties of metal-ceramic composites with reinforcing ceramic inclusions of different shapes. Values of effective sound velocities, elastic moduli and elastic limits of investigated materials are obtained, and the character of the dependence of the effective elastic and strength properties on the structure parameters of composites is determined. The simulation results show that values of effective mechanical characteristics weakly depend on the shape of reinforcing inclusions and mainly are defined by their volume concentration

Kinematics of a relativistic particle with de Sitter momentum space

We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and equations of motion for such free particle. We study the action of deformed relativistic symmetries on the phase space and derive explicit formulas for the action of the deformed Poincare' group. Finally we provide a discussion on parametrization of the particle worldlines stressing analogies and differences with ordinary relativistic kinematics.Comment: RevTeX, 12 pages, no figure

Response evolution of a tetrachiral metamaterial unit cell under architectural transformations

This paper studies a mechanical metamaterial with tetrachiral topology by mathematical modeling. Chirality is the property of an object that makes the object distinguishable from its mirror image; chirality can be left‐ or right‐handed. The mechanical response of two metamaterial unit cells with different configurations (patterns A and B) is investigated. It is found that the cubic cell with a regular pattern A exhibits orthotropic mechanical behavior under loading along three coordinate axes. An irregular pattern B differs from pattern A in that the upper face of the unit cell has an opposite chirality. This architectural transformation is considered as a topological defect, which enhances the twisting effect in the loaded metamaterial. Analysis of displacements and stresses shows that the mechanical behavior of the pattern B cell is described by the model of a transversely isotropic material. The orthotropic and transversely isotropic behavior of the cells of given configurations is also confirmed by the values of the effective elastic constants. Microstructural geometry and mechanical deformation of metamaterials are shown to be closely related. It is shown that a topological defect in a unit cell of a tetrachiral metamaterial strongly determines its twisting behavior

Investigation of failure mechanism of Al2O3 specimens subjected to three-point bending test

Experimental loading and FEM simulation-based approach at macroscale are utilized to investigate the failure mechanisms of Al2O3 ceramics. Experimental characterization of the microstructure is carried out using SEM. Recently the mesoscale models of a representative volume of porous alumina ceramics were built on the basis of grain and pore distribution patterns and subjected to uniaxial loading in order to determine effective mechanical characteristics which are utilized for macroscopic simulation in this work. Pre-fracture behavior of specimens undergoes the Drucker-Prager model with non-associated plastic flow rule. Experimental and numerical simulation fracture patterns show that material exhibits predominantly mode I, sometimes passing to mixed mode I+II of crack propagation. Comparison of experimental data and numerical simulation data gives a good agreement

Modal testing circuit board assembly of an electronic apparatus by laser vibrometry

The operating capacity and service life of printed circuit boards in various electronic equipment and devices depends on their ability to resist vibroacoustic loads, including vibration and acoustic noises. In this paper, non-contact laser vibrometry has been applied to perform the modal analysis of a circuit board assembly in order to identify its vulnerable spots and to find solutions to protect the assembly from external vibroacoustic loads. A broadband periodic chirp signal was used to excite vibration, which enabled a rapid generation of results. The paper provides data on eigenfrequencies, vibration velocity fields, and vibration displacement profiles. Frequency ranges have been determined in which eigenfrequencies with the highest vibration amplification lie. The obtained data can be used to develop a quality control technique for printed circuit boards and to optimize their construction as early as the design stage

The principle of relative locality

We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of momentum space with a metric compatible connection and constant curvature.Comment: 12 pages, 3 figures; in version 2 one reference added and some minor modifications in sects. II and III mad