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In our previous study (Part I), the anti-plane steady-state hyperbolic mode III fracture of a magneto-flexoelectric material was solved for the displacement, the polarization, and the magnetic fields. The solution, however, was based on the assumption of the development of strain discontinuities, and the propagation of the crack-tip was related to a critical shear strain. However, in the current study, the asymptotic details of the fields close to the crack-tip were investigated. The asymptotic analysis assumes strain continuity at the crack-tip (discontinuity in the strain gradients) and reveals the existence of a positive dynamic J-integral. The asymptotic analysis was performed not only for hyperbolic but also for elliptic conditions, and the energy release rate was calculated as a function of the crack-tip velocity in both regimes. These results are very different from those predicted by classical singular elastodynamics, where the dynamic J-integral is zero when super-shear is attained and there can be only an elliptic solution. Moreover, the results are very useful for couple-stress elastodynamics where equivalent length scales are present due to the analogy with flexoelectricity. [ABSTRACT FROM AUTHOR]

Analytical solutions to the classical Mandel's problem play an important role in understanding Biot's theory of poroelasticity and validating geomechanics numerical algorithms. In this paper, existing quasi-static poroelastic solutions to this problem are extended to the dual-porosity dual-permeability poroelastodynamics solution which considers inertial effects for a naturally fractured and fluid-saturated sample subjected to a harmonic excitation. The solution can generate the associated elastodynamics and poroelastodynamics solutions as special cases. A naturally fractured Ohio sandstone is selected to demonstrate the newly derived solution. The elastodynamics, poroelastodynamics, and dual-porosity poroelastodynamics solutions are compared to illustrate the effects of fluid-solid coupling and the natural fractures. The rock sample behaves in drained condition at low frequencies when the oscillation has insignificant impedance effects on fluid movement. Compared to the other two solutions, the dual-porosity solution predicts the largest amplitude of displacement at low frequencies when the response is predominantly controlled by the stiffness. The Mandel-Cryer effect is observed in both rock matrix and fractures and occurs at a lower frequency in rock matrix because it is easier to build up pore pressure in lower-permeability rock matrix. At high frequencies, pore fluids are trapped and the rock sample behaves in an undrained state. At the resonance frequencies, the elastodynamics solution provides the largest amplitude of displacement, followed by the poroelastodynamics and dual-porosity poroelastodynamics solution. This is because of the dissipation caused by the presence of both fluid and fractures. [ABSTRACT FROM AUTHOR]

The destabilization of the steady-state regime of two semi-infinite half-spaces of different elastic coefficients sliding upon each other has been theoretically investigated when a rate-and-state friction constitutive law controls the sliding. In the framework of linear and isotropic elastodynamics, the effect of the frictional constitutive law has been investigated onto the development of self-excited oscillations as well as the influence of the shear modulus difference between the two materials. The possibility of existence of a stick-slip regime and the conditions for the loss-of-contact are finally discussed. [ABSTRACT FROM AUTHOR]

Recently, patterned surfaces (elastodynamic meta-surfaces) were shown to cause mechanical wave depolarization resulting in conversion of uniaxial waves to multiaxial vibrations. Frictional oscillators loaded in multiple directions provide more tailorable damping scheme when compared to uniaxially loaded equivalents. This paper utilizes wave depolarization properties of patterned surfaces in tuning frictional damping. In particular, two-dimensional (2D) motion achieved by anisotropic wave reflection and depolarization across patterned surfaces is exerted on a simple friction oscillator; and frictional energy dissipation is studied using the homogenization theory and mechanics of a simple friction oscillator under macro and microslip conditions. The degree of depolarization is shown to control the extent of frictional shakedown (no-dissipation) zones and magnitude of energy dissipation for different incident wave frequencies and amplitudes. Transmission of the depolarized waves from the patterned surface to the friction oscillator enables higher and more uniform frictional damping for broader loading conditions. Uniform damping facilitates predictive linear dynamic models, and tuning the magnitude of damping permits efficient and robust wave attenuation, and energy transfer and localization in dynamic applications. A discussion on modeling assumptions and practical utilization of this potential is also provided. The presented potential of tuning frictional dissipation from very low to high values by simple surface patterns suggests that more sophisticated surface patterns can be designed for spatially varying frequency-dependent wave attenuation. [ABSTRACT FROM AUTHOR]

The diffraction of elastic harmonic waves by a finite plane tunnel crack is studied. A solution is derived from an analysis of the integral equations describing the problem, using the Wiener-Hopf technique and the method of compound asymptotic expansions. Taking into account the successive reflections of Rayleigh waves from crack tips, an approximate analytical solution is expressed in a closed-form that is computationally effective and yields accurate results in the resonance region of dimensionless wave numbers. Both direct and inverse scattering problems are considered. [ABSTRACT FROM AUTHOR]

Parallel kinematic machines (PKMs) have been proposed as an alternative solution for high-speed machining (HSM) tool for several years. However, their dynamic characteristics are still considered an issue for practice application. Considering the three prismatic--revolute--spherical (3-PRS) PKM design as a typical compliant parallel device, this paper applies substructure synthesis strategy to establish an analytical elastodynamic model for the device. The proposed model considers the effects of component compliances and kinematic pair contraints so that it can predict the dynamic characteristics of the 3-PRS PKM. Based on eigenvalue decomposition of the characteristic equations, the natural frequencies and corresponding vibration modes at a typical configuration are analyzed and verified by numerical simulations. With an algorithm of workspace partitions combining with eigenvalue decompositions, the distributions of lower-order natural frequencies throughout the workspace are computed to reveal a strong dependency of dynamic characteristics on mechanism's configurations. In addition, the effects of the radii of the platform and the base along with the cross section of the limb on lower-order natural frequencies are analyzed to provide useful information during the early design stage. At last, frequency response analysis for the tool center point (TCP) is worked out based on the elastodynamic model to provide primary guideline for cutting chatter avoidance. [ABSTRACT FROM AUTHOR]

As a newly invented parallel kinematic machine (PKM), Exechon has attracted intensive attention from both academic and industrial fields due to its conceptual high performance. Nevertheless, the dynamic behaviors of Exechon PKM have not been thoroughly investigated because of its structural and kinematic complexities. To identify the dynamic characteristics of Exechon PKM. an elastodynamic model is proposed with the substructure synthesis technique in this paper. The Exechon PKM is divided into a moving platform subsystem, a fixed base subsystem and three limb subsystems according to its structural features. Differential equations of motion for the limb subsystem are derived through finite element (FE) formulations by modeling the complex limb structure as a spatial beam with corresponding geometric cross sections. Meanwhile, revolute, universal, and spherical joints are simplified into virtual lumped springs associated with equivalent stiffnesses and mass at their geometric centers. Differential equations of motion for the moving platform are derived with Newton's second law after treating the platform as a rigid body due to its comparatively high rigidity. After introducing the deformation compatibility conditions between the platform and the limbs, governing differential equations of motion for Exechon PKM are derived. The solution to characteristic equations leads to natural frequencies and corresponding modal shapes of the PKM at any typical configuration. In order to predict the dynamic behaviors in a quick manner, an algorithm is proposed to numerically compute the distributions of natural frequencies throughout the workspace. Simulation results reveal that the lower natural frequencies are strongly position-dependent and distributed axial-symmetrically due to the structure symmetry of the limbs. At the last stage, a parametric analysis is carried out to identify the effects of structural, dimensional, and stiffness parameters on the system's dynamic characteristics with the purpose of providing useful information for optimal design and performance improvement of the Exechon PKM. The elastodynamic modeling methodology and dynamic analysis procedure can be well extended to other over constrained PKMs with minor modifications. [ABSTRACT FROM AUTHOR]

Homogeneous nucleation of dislocations is the dominant dislocation generation mechanism at strain rates above 108 s-1 at those rates, homogeneous nucleation dominates the plastic relaxation of shock waves in the same way that Frank-Read sources control the onset of plastic flow at low strain rates. This article describes the implementation of homogeneous nucleation in dynamic discrete dislocation plasticity (D3P), a planar method of discrete dislocation dynamics (DDD) that offers a complete elastodynamic treatment of plasticity. The implemented methodology is put to the test by studying four materials--Al, Fe, Ni, and Mo--that are shock loaded with the same intensity and a strain rate of 1010 s-1. It is found that, even for comparable dislocation densities, the lattice shear strength is fundamental in determining the amount of plastic relaxation a material displays when shock loaded. [ABSTRACT FROM AUTHOR]

The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and energy in the case of undamped linear elastodynamics problems, and an "energy-like measure" in the case of undamped acoustic problems. These conservation properties, thus, provide a rational basis for using this algorithm. In linear elastodynamics problems, variants of the trapezoidal rule that incorporate "high-frequency" dissipation are often used, since the higher frequencies, which are not approximated properly by the standard displacement-based approach, often result in unphysical behavior. Instead of modifying the trapezoidal algorithm, we propose using a hybrid finite element framework for constructing the stiffness matrix. Hybrid finite elements, which are based on a two-field variational formulation involving displacement and stresses, are known to approximate the eigenvalues much more accurately than the standard displacement-based approach, thereby either bypassing or reducing the need for high-frequency dissipation. We show this by means of several examples, where we compare the numerical solutions obtained using the displacementbased and hybrid approaches against analytical solutions. [ABSTRACT FROM AUTHOR]

Energy losses in an internal combustion engine are either thermal or parasitic. The latter are the mechanical inefficiencies, chiefly as the result of generated friction. Nearly half of these losses are attributed to the piston-cylinder system. During idle and at low engine speeds, friction is the major contributor to the overall engine losses. In particular, the rather small top compression ring accounts for a disproportionate share. Therefore, detailed understanding of compression ring tribology/dynamics (referred to as tribodynamics) is essential. Moreover, the ring's primary sealing function may be breached by its elastodynamic behavior. The reported analyses in literature do not account for the transient nature of ring elastodynamics, as an essential feature of ring-bore tribology. The transient in-plane dynamics of incomplete rings are introduced in the analysis and verified using a finite element analysis (FEA) model, in order to address this shortcoming. The methodology is then coupled with the tribological analysis of the top compression ring. Comparison is made with experimental measurements which show the validity of the proposed method. The radial in-plane elastodynamic response of the ring improves the accuracy of the frictional power loss calculations. [ABSTRACT FROM AUTHOR]

In this study, the concept of the fracture mechanics is used to solve the: (i) frictionless purely normal contact and (ii) the similar material contact under the mutual actions of the normal and tangential load. Considering the contact region is simply connected, the out-of-contact regions can be treated as periodic collinear cracks. Through evaluating the stress intensity factor (SIF), we are able to obtain the size and location of the contact/out-of-contact region. Then, the normal traction, shear traction and interfacial gap can be directly determined by the Green's function of the periodic collinear crack. In the case of frictionless purely normal contact, the new approach is applied to two classic problems, namely, the Westergaard problem (sinusoidal waviness punch) and the periodic flat-end punch problem. Then, the sinusoidal waviness contact pair in the full stick and the partial slip conditions under the mutual actions of the normal and tangential loads are solved by the newly developed approach. [ABSTRACT FROM AUTHOR]