Generalized diagonalization of matrices over quaternion field

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Uniaxial experimental study of the acoustic emission and deformation behavior of composite rock based on 3D digital image correlation (DIC)

In this paper, uniaxial compression tests were carried out on a series of composite rock specimens with different dip angles, which were made from two types of rock-like material with different strength. The acoustic emission technique was used to monitor the acoustic signal characteristics of composite rock specimens during the entire loading process. At the same time, an optical non-contact 3 D digital image correlation technique was used to study the evolution of axial strain field and the maximal strain field before and after the peak strength at different stress levels during the loading process. The effect of bedding plane inclination on the deformation and strength during uniaxial loading was analyzed. The methods of solving the elastic constants of hard and weak rock were described. The damage evolution process, deformation and failure mechanism, and failure mode during uniaxial loading were fully determined. The experimental results show that the θ = 0?–45?specimens had obvious plastic deformation during loading, and the brittleness of the θ = 60?–90?specimens gradually increased during the loading process. When the anisotropic angle θincreased from 0?to 90?, the peak strength, peak strain,and apparent elastic modulus all decreased initially and then increased. The failure mode of the composite rock specimen during uniaxial loading can be divided into three categories:tensile fracture across the discontinuities(θ = 0?–30?), slid-ing failure along the discontinuities(θ = 45?–75?), and tensile-split along the discontinuities(θ = 90?). The axial strain of the weak and hard rock layers in the composite rock specimen during the loading process was significantly different from that of the θ = 0?–45?specimens and was almost the same as that of the θ = 60?–90?specimens. As for the strain localization highlighted in the maximum principal strain field, the θ = 0?–30?specimens appeared in the rock matrix approximately parallel to the loading direction,while in the θ = 45?–90?specimens it appeared at the hard and weak rock layer interface.     

On the propagation of elastic waves in a multiperiodically reinforced medium

By a multiperiodically reinforced medium (multiperiodic composite) we mean a composite in which the matrix material is reinforced by two or more families of periodically spaced fibres. Moreover, at least along one direction the periods corresponding to different families are different. An example of this composite is shown in Fig. 1, where along the x ¹-axis we deal with two different periods . The aim of the contribution is twofold. First, we propose a macroscopic (averaged) model of a multiperiodic composite, describing the effect of period lengths on the overall dynamic behaviour of the medium, in contrast to the known homogenized models. Second, we apply this model to the analysis of elastic waves propagating across a composite reinforced by two pairs of families of parallel periodically spaced fibres with different periods along certain direction.     

A Helmholtz/Weyl Decomposition in Energy Space

For a bounded region in a Helmholtz/Weyl decomposition of the Sobolev space is given,with orthogonality with respect to the strain-energy inner product of elasticity (anisotropic or isotropic).     

Existence of a Solution “in the Large” for Ocean Dynamics Equations

For the system of equations describing the large-scale ocean dynamics, an existence and uniqueness theorem is proved “in the large”. This system is obtained from the 3D Navier–Stokes equations by changing the equation for the vertical velocity component u ₃ under the assumption of smallness of a domain in z-direction, and a nonlinear equation for the density function ρ is added. More precisely, it is proved that for an arbitrary time interval [0, T], any viscosity coefficients and any initial conditions

Displacement and Dissolution Characteristics of CO$$_{}$$/Brine System in Unconsolidated Porous Media

This study investigated the dynamic displacement and dissolution of \(\hbox {CO}_{2}\) in porous media at 313 K and 6/8 MPa. Gaseous (\(\hbox {gCO}_{2}\)) at 6 MPa and supercritical \(\hbox {CO}_{2 }(\hbox {scCO}_{2}) \) at 8 MPa were injected downward into a glass bead pack at different flow rates, following upwards brine injection. The processes occurring during \(\hbox {CO}_{2}\) drainage and brine imbibition were visualized using magnetic resonance imaging. The drainage flow fronts were strongly influenced by the flow rates, resulting in different gas distributions. However, brine imbibition proceeded as a vertical compacted front due to the strong effect of gravity. Additionally, the effects of flow rate on distribution and saturation were analyzed. Then, the front movement of \(\hbox {CO}_{2}\) dissolution was visualized along different paths after imbibition. The determined \(\hbox {CO}_{2}\) concentrations implied that little \(\hbox {scCO}_{2}\) dissolved in brine after imbibition. The dissolution rate was from \(10^{-8}\) to \(10^{-9}\, \hbox {kg}\, \hbox {m}^{-3} \, \hbox {s}^{-1}\) and from \(10^{-6}\) to \(10^{-8}\, \hbox {kg}\, \hbox {m}^{-3} \, \hbox {s}^{-1}\) for \(\hbox {gCO}_{2}\) at 6 MPa and \(\hbox {scCO}_{2 }\) at 8 MPa, respectively. The total time for the \(\hbox {scCO}_{2}\) dissolution was short, indicating fast mass transfer between the \(\hbox {CO}_{2}\) and brine. Injection of \(\hbox {CO}_{2}\) under supercritical conditions resulted in a quick establishment of a steady state with high storage safety.     

Solution of A 2-D weak singular integral equation with constraint

In this paper, the solution of a 2-D weak singular integral equation of the first kind

Diffusion Driven Accelerated Stress Corrosion Cracking in an Acrylic Polymer

The dynamic evolution and mechanism of accelerated stress corrosion cracking (aSCC) in anacrylic (PMMA–poly methyl 2-methylpropenoate) polymer sample have been exploited quantitatively, in absence of external mechanical load. Unusually fast propagation of solvent induced cracks in micro-machined sections of the material has been monitored by microscopic video imaging of a test device. Crack emanation from milled micro-channels was precisely triggered by brief surface wetting with acetone solvent. The crack propagation period persists over a time span of approximately 1 min, comprises a final crack length of 0.2–0.3 mm, and an associated crack growth rate that decreases from $2 \times 10^{-5}$ to $10^{-6}$ m/s. The temporal crack evolution scales in accord with 1-dim solvent diffusion along the flaw, super imposed with the residual stress field. Optically recorded birefringence, as well as finite element structure mechanic simulation, identified residual tensile stress in the crack zone as the driving force. The residual stress intensity factor $\Delta K$ was determined to 1–2 MPa  ${\rm m}^{1/2}$ . The aSCC (accelerated stress corrosion cracking) in the material originates from a detrimental combination of residual stress, induced by surface milling; stress induced fast diffusion of the acetone solvent into the material and an associated degradation of structure-mechanic parameters.     

Almost Periodicity in an Ecological Model with <Emphasis Type="Italic">M</Emphasis>-Predators and <Emphasis Type="Italic">N</Emphasis>-Preys by “Pure-Delay Typ” System

By using comparison theorem and constructing suitable Lyapunov functional, we study the following periodic Lotka–Volterra model with M-predators and N-preys by pure-delay type

Numerical study of a nonlinear integrodifferential equation

I.IntroductionItiswell-knobal.nthatKorteweg-deVriesequationisacanonicalmodeltodescribethebalanceofthenonlineareffectandthedispersiveeffectofaphysicalsystem.Thisequationpossessestheso-called'soliton"solution,whichhasbeenfoundnumericallybyZabuskyandKruskall'].Ho-c'Jlever,sometimesthebalanceofnonlinearityanddispersionofasystemmayleadtoa,integroditTerentialequationinsteadofadifferentialequation.Forinstance,inthestudyofvortexbreakdownofanunboundedrotatingfluidLeibovich12]derivedfollowingnonline…     

Constitutive modeling of fiber composites with a soft hyperelastic matrix

This paper presents an experimental and numerical study of unidirectional carbon fiber composites with a silicone matrix, loaded transversally to the fibers. The experiments show nonlinear behavior with significant strain softening under cyclic loading. The numerical study uses a plane-strain finite element continuum model of the composite material in which the fiber distribution is based on experimental observations and cohesive elements allow debonding to take place at the fiber/matrix interfaces. It is found that accurate estimates of the initial tangent stiffness measured in the experiments can be obtained without allowing for debonding, but this feature has to be included to capture the non-linear and strain-softening behavior.     

Numerical homogenization of elastic and thermal material properties for metal matrix composites (MMC)

A two-scale material modeling approach is adopted in order to determine macroscopic thermal and elastic constitutive laws and the respective parameters for metal matrix composite (MMC). Since the common homogenization framework violates the thermodynamical consistency for non-constant temperature fields, i.e., the dissipation is not conserved through the scale transition, the respective error is calculated numerically in order to prove the applicability of the homogenization method. The thermomechanical homogenization is applied to compute the macroscopic mass density, thermal expansion, elasticity, heat capacity and thermal conductivity for two specific MMCs, i.e., aluminum alloy Al2024 reinforced with 17 or 30 % silicon carbide particles. The temperature dependency of the material properties has been considered in the range from 0 to \(500{\,}^\circ \mathrm {C}\), the melting temperature of the alloy. The numerically determined material properties are validated with experimental data from the literature as far as possible.     

An L∞ bound for solutions of the Cahn-Hilliard equation

In this paper we consider the equation

Closedness and normal solvability of an operator generated by a degenerate linear differential equation with variable coefficients

For a linear operator generated by the differential equation

The evaluation of integrals containing a parameter

Summary A number of methods for obtaining expansions and approximations to an integral containing a parameter are expounded, and each illustrated by evaluating the function      

The study on the compressive behavior of ptfe/al energetic composite

金属/氟聚合物含能复合材料是一类新型的高级含能材料. 研究了室温下Al含量和应变 率对PTFE/Al含能复合材料压缩性能和反应性能的影响,所加载的应变率为6\times 10^{-3}s^{-1}\sim8\times 10^{3}s^{ -1}. 材料压缩性能的应变 率效应明显：与静态加载相比,动态加载下材料模量和强度明显提 高,但应变降低. 材料的损伤过程主要包括塑性变形、开裂和反应3部分. 随着Al含量的增 加,材料准静态和动态压缩强度均呈先升后降的趋势,在 Al含量为35\%时达到 最高值102.6 MPa和154 MPa; 引发反应所需加载的应变率增加,但对应的应力值 差别不明显,基本在165 MPa左右, 材料引发后反应完全性降低.     

Explicit Effective Constants for an Inhomogeneous Porothermoelastic Medium

An arbitrary anisotropic micro-inhomogeneous (composite) poroelastic medium is considered, containing a random set of ellipsoidal inhomogeneities with different poroelastic characteristics. The properties of these constituents are described by the linear porothermoelastic theory of Biot. One of the self-consistent schemes named effective field method is used to develop explicit expressions for the effective porothermoelastic constants (tensor of the frame elastic compliances , tensor of the generalized Skempton’s coefficients , tensor of thermal expansion coefficients , Biot’s constants , and the heat capacity at constant stress for the static porothermoelastic theory. It is shown that for two components composite porous material these expressions are interconnected and can be expressed only via the components of tensor . Some special cases are considered for the isotropic main material (matrix).     

Resolvent Estimates for High-Contrast Elliptic Problems with Periodic Coefficients

We study the asymptotic behaviour of the resolvents \({(\mathcal{A}^\varepsilon+I)^{-1}}\) of elliptic second-order differential operators \({{\mathcal{A}}^\varepsilon}\) in \({\mathbb{R}^d}\) with periodic rapidly oscillating coefficients, as the period \({\varepsilon}\) goes to zero. The class of operators covered by our analysis includes both the “classical” case of uniformly elliptic families (where the ellipticity constant does not depend on \({\varepsilon}\)) and the “double-porosity” case of coefficients that take contrasting values of order one and of order \({\varepsilon^2}\) in different parts of the period cell. We provide a construction for the leading order term of the “operator asymptotics” of \({(\mathcal{A}^\varepsilon+I)^{-1}}\) in the sense of operator-norm convergence and prove order \({O(\varepsilon)}\) remainder estimates.