Effect Of Characteristic Length Research Articles

Crystal cluster forming process under rarefied gas and low temperature environment

Aerospace engine plume flow under high altitude environment generates crystal due to low atmosphere temperature, thus causing variation on flow field and radiation properties. In order to gain better understanding on crystal generation and growth process, this article fundamentally establishes thermal motion phase change (TMPC) model based on molecular thermal motion. Direct calculation on molecular motion in phase change process takes influence of large scaled molecular free path caused by rarefied environment into consideration. The effect of temperature, H2O vapor number density, and characteristic length on phase change process is studied. According to the results, characteristic length determines non-continuum degree quantitatively under rarefied gas condition. Increasing characteristic length decreases phase change time before reaching steady state. Crystal number density decreases when working condition is near saturation condition, while crystal radius shows contrary trend. The effect of characteristic length on crystal cluster quantity and radius variation is prominent under low vapor number density condition, for increasing vacuum effect caused by decreasing gas molecules quantity. Existence of other gas components contamination obstructs H2O vapor molecules thermal motion, thus decreasing non-continuum effect on phase change process, where variation of characteristic length shows relatively limited influence on crystal cluster properties and phase change time.

Static and Dynamic Analysis of a Piezoelectric Semiconductor Cantilever Under Consideration of Flexoelectricity and Strain Gradient Elasticity

In this work, the static and dynamic response of a piezoelectric semiconductor cantilever under the transverse end force with consideration of flexoelectricity and strain gradient elasticity is systematically investigated. The one-dimensional governing equations and the corresponding boundary conditions are derived based on Hamilton’s principle. After that, combining with the linearized equations for the conservation of charge, the effects of characteristic length and flexoelectric coefficient on the working performance of a ZnO nanowire are demonstrated as a numerical case, including the static mechanical and electric fields, natural frequencies, and the frequency–response characteristics at resonances. The results indicate that the flexoelectric effect has a great influence on the electric properties of the nanowire, while the strain gradient effect directly contributes to its mechanical properties. To some extent, the increase in characteristic length is equivalent to the stiffness strengthening. The qualitative results and quantitative data are beneficial for revealing the underlying physical mechanism and provide guidance for the design of piezoelectric semiconductor devices.

Theoretical Study on the Dynamic Behavior of a Plate-Like Micro-Cantilever with Multiple Particles Attached.

In this study, the dynamic characteristics of a plate-like micro-cantilever beam attached with multiple concentrated masses are studied. The vibration modes of the cantilever plate are represented by combinations of beam functions. Using classical mechanics (the effect of size is not considered) and the corrected Cosserat’s theorem (the effect of size is considered), we employ the Lagrange equations to establish a dynamic model of the plate-like micro-cantilever beam attached with multiple concentrated masses. The accuracy of the model proposed in this paper is verified by comparing with the results of published literature. Then, the natural frequencies of the cantilever plates are calculated with self-compiled algorithms, and the results of the plates with 1–5 masses are displayed. The results are in high accordance with the exact solution, and all errors are within 0.5%. The analysis shows that the proposed model and analysis method converges quickly and is highly efficient. In addition, the effects of characteristic lengths, Poisson's ratios and plate thickness on the micro-cantilever plate’s resonant frequency for the first five modes are analyzed.

The effect of characteristic length on mean free path for confined gases

Molecular Dynamics simulations are performed to investigate the influence of system boundaries and characteristic length (L) of the system on the mean free path (MFP) of rarefied gas confined to the walls of a nano-channel. Isothermal Lennard-Jones fluid confined between Reflective walls and platinum walls at different number densities (0.31 atoms/nm3 and 1.61 atoms/nm3) are independently considered. The MFP is calculated by the Lagrangian approach of tracking the trajectory of each atom and averaging the distance between successive collisions. The percentage of fluid–wall collisions is observed to predominate over fluid–fluid collisions at high levels of rarefaction. The influence of L (varying from 6 nm to 16 nm) on MFP is examined in this regime. At lower Knudsen number (Kn), it is observed that the effect of L on MFP is minimal. However, at higher rarefaction the characteristic dimension influences the MFP significantly for various wall configurations.

Effect of Characteristic Lengths of Fracture on Thermal Crack Patterns

AbstractApproximately uniformly spaced cracking occurs in many different materials and processes during thermal or drying shrinkage. Such cracks may occur when a slab of material restrained at the bottom is subjected to a sudden reduction in temperature at the top. Previous research indicates that the crack patterns obtained depend on the Griffith crack length for a shrinking solid. This paper shows that for materials exhibiting elastic-plastic fracture behavior, the fracture energy, Young’s modulus, and tensile strength in combination form a second characteristic length of fracture of the material that has a significant impact on the cracks formed.

Velocity dispersion in an elastic plate with microstructure: effects of characteristic length in a couple stress model

Microstructural effects become important, when dimensions of the heterogeneous material are comparable to the length scale of microstructure and the state of stress needs to be defined in a non-local manner. Linear theory of elasticity, which is associated with the concept of homogeneity of material and local stresses, cannot describe the behavior of the materials with microstructures. In this study, Couple stress theory of elasticity has been employed to capture the size effects on the propagation of Lamb waves in an elastic plate with microstructure. Effects on the dispersion curves of Lamb waves are studied, when the characteristic length of the material is comparable to cell size. The governing equations of couple stress theory, involving stresses and couple stresses are solved to study the impact of different characteristic lengths, comparable with cell size. Since bone is a material with microstructure, so for numerical calculations and graphical representation of the results, the plate is considered to have mechanical properties typically used for bones.

Lamb waves in micropolar thermoelastic solid plates immersed in liquid with varying temperature

In the present paper the theory of micropolar generalized thermoelastic continua has been employed to study the propagation of plane waves in micropolar thermoelastic plates bordered with inviscid liquid layers (or half-spaces) with varying temperature on both sides. The secular equations in closed form and isolated mathematical conditions are derived and discussed. Thin plate and short wave length results have also been deduced under different cases and situations and discussed as special cases of this work. The results in case of conventional coupled and uncoupled theories of thermoelasticity can be obtained both in case of micropolar elastic and elastokinetics from the present analysis by appropriate choice of relevant parameters. The various secular equations and relevant relations have been solved numerically by using functional iteration method in order to illustrate the analytical developments. Effect of characteristic length and coupling factors have also been studied on phase velocity. The computer simulated results in case of phase velocity, attenuation coefficient and specific loss of symmetric and skew symmetric are presented graphically.

On the effects of characteristic lengths in bending and torsion on Mode III crack in couple stress elasticity

The problem of a stationary semi-infinite crack in an elastic solid with microstructures subject to remote classical K III field is investigated in the present work. The material behavior is described by the indeterminate theory of couple stress elasticity developed by Koiter. This constitutive model includes the characteristic lengths in bending and torsion and thus it is able to account for the underlying microstructure of the material as well as for the strong size effects arising at small scales. The stress and displacement fields turn out to be strongly influenced by the ratio between the characteristic lengths. Moreover, the symmetric stress field turns out to be finite at the crack tip, whereas the skew-symmetric stress field displays a strong singularity. Ahead of the crack tip within a zone smaller than the characteristic length in torsion, the total shear stress and reduced tractions occur with the opposite sign with respect to the classical LEFM solution, due to the relative rotation of the microstructural particles currently at the crack tip. The asymptotic fields dominate within this zone, which however has limited physical relevance and becomes vanishing small for a characteristic length in torsion of zero. In this limiting case the full-field solution recovers the classical K III field with square-root stress singularity. Outside the zone where the total shear stress is negative, the full-field solution exhibits a bounded maximum for the total shear stress ahead of the crack tip, whose magnitude can be adopted as a measure of the critical stress level for crack advancing. The corresponding fracture criterion defines a critical stress intensity factor, which increases with the characteristic length in torsion. Moreover, the occurrence of a sharp crack profile denotes that the crack becomes stiffer with respect to the classical elastic response, thus revealing that the presence of microstructures may shield the crack tip from fracture.

Effect of a characteristic length on crack spacing in a reinforced concrete bar under tension

The paper presents quasi-static FE-simulations of the crack formation in a reinforced concrete bar without stirrups subject to tension. The material was modeled with a continuum smeared crack model using an elasto-plastic constitutive law. A linear Rankine criterion with isotropic softening and associated flow rule was adopted in a tensile regime. To ensure the mesh-independency, the softening parameter was enhanced by a characteristic length of micro-structure by means of a non-local theory. Attention was laid to the effect of a different characteristic length of micro-structure and initial bond-slip stiffness on the spacing of localized zones.

High-Gradient Modeling for Love Wave Propagation in Geological Materials

Based on a microstructural approach, geological material, owing to its discrete nature, can be represented by an equivalent continuum of the high-gradient type. The high-gradient continuum differs from the perfectly elastic continuum by having a characteristic length scale that is an intrinsic property of the material. Using the high-gradient stress-strain relationship, we formulate a fourth-order wave equation to describe the propagation of a Love-wave in a two-layer medium. We employ Hamilton's principle to derive the additional boundary conditions involved in the differential equation. The differential equation is then solved to study the effects of characteristic length on the wave propagation in geological material. Comparisons are made between the predicted and observed wave velocities in a two-layer geological medium during an earthquake.

Effect of Characteristic Length on Stress Distribution of a Fiber-Reinforced Material

Couple stresses may be induced under certain loading conditions in a fiber-reinforced composite material. It may affect the over all stress field of the composite. This paper shows the stress field as affected by the relationship of the characteristic lengths of the constituents of the fiber-reinforced material. Also, a comparison between this stress distribution and the stresses based on classical analysis is made.