A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory

A size-dependent model for bending and free vibration of functionally graded plate is developed based on the modified couple stress theory and sinusoidal shear deformation theory. In the former theory, the small scale effect is taken into consideration, while the effect of shear deformation is accounted for in the latter theory. The equations of motion and boundary conditions are derived from Hamilton’s principle. Analytical solutions for the bending and vibration problems of simply supported plates are obtained. Numerical examples are presented to illustrate the influences of small scale on the responses of functionally graded microplates. The results indicate that the inclusion of small scale effects results in an increase in plate stiffness, and consequently, leads to a reduction of deflection and an increase in frequency. Such small scale effects are significant when the plate thickness is small, but become negligible with increasing plate thickness

Shock Hugoniot of Single Crystal Copper

The shock Hugoniot of single crystal copper is reported for stresses below 66 GPa. Symmetric impact experiments were used to measure the Hugoniots of three different crystal orientations of copper, [100], [110], [111]. The photonic doppler velocimetry (PDV) diagnostic was adapted into a very high precision time of arrival detector for these experiments. The measured Hugoniots along all three crystal directions were nearly identical to the experimental Hugoniot for polycrystalline Cu. The predicted orientation dependence of the Hugoniot from MD calculations was not observed. At the lowest stresses, the sound speed in Cu was extracted from the PDV data. The measured sound speeds are in agreement with values calculated from the elastic constants for Cu

Three-dimensional coherent X-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms

Ultra-low density polymers, metals, and ceramic nanofoams are valued for their high strength-to-weight ratio, high surface area and insulating properties ascribed to their structural geometry. We obtain the labrynthine internal structure of a tantalum oxide nanofoam by X-ray diffractive imaging. Finite element analysis from the structure reveals mechanical properties consistent with bulk samples and with a diffusion limited cluster aggregation model, while excess mass on the nodes discounts the dangling fragments hypothesis of percolation theory.Comment: 8 pages, 5 figures, 30 reference

Densification and residual stress induced by CO2 laserbased mitigation of SiO2 surfaces

ABSTRACT Knowing the ultimate surface morphology resulting from CO 2 laser mitigation of induced laser damage is important both for determining adequate treatment protocols, and for preventing deleterious intensification upon subsequent illumination of downstream optics. Physical effects such as evaporation, viscous flow and densification can strongly affect the final morphology of the treated site. Evaporation is a strong function of temperature and will play a leading role in determining pit shapes when the evaporation rate is large, both because of material loss and redeposition. Viscous motion of the hot molten material during heating and cooling can redistribute material due to surface tension gradients (Marangoni effect) and vapor recoil pressure effects. Less well known, perhaps, is that silica can densify as a result of structural relaxation, to a degree depending on the local thermal history. The specific volume shrinkage due to structural relaxation can be mistaken for material loss due to evaporation. Unlike evaporation, however, local density change can be reversed by post annealing. All of these effects must be taken into account to adequately describe the final morphology and optical properties of single and multiple-pass mitigation protocols. We have investigated, experimentally and theoretically, the significance of such densification on residual stress and under what circumstances it can compete with evaporation in determining the ultimate post treatment surface shape. In general, understanding final surface configurations requires taking all these factors including local structural relaxation densification, and therefore the thermal history, into account. We find that surface depressions due to densification can dominate surface morphology in the non-evaporative regime when peak temperatures are below 2100K

An Assessment of Molecular Dynamic Force Fields for Silica for Use in Simulating Laser Damage Mitigation

We compare force fields (FF's) that have been used in molecular dynamic (MD) simulations of silica in order to assess their applicability for use in simulating IR-laser damage mitigation. Although pairwise FF?s obtained by fitting quantum mechanical calculations such as the BKS and CHIK potentials have been shown to reproduce many of the properties of silica including the stability of silica polymorphs and the densification of the liquid, we show that melting temperatures and fictive temperatures are much too high. Softer empirical force fields give liquid and glass properties at experimental temperatures but may not predict all properties important to laser mitigation experiments

Threats to ICF reactor materials: computational simulations of radiation damage induced topological changes in fused silica

Abstract We have performed molecular dynamics simulations of radiation damage in fused silica. In this study, we discuss the role of successive cascade overlap on the saturation and self-healing of oxygen vacancy defects in the amorphous fused silica network. Furthermore, we present findings on the topological changes in fused silica due to repeated energetic recoil atoms. These topological network modifications consistent with experimental Raman spectroscopic observation on neutron and ion irradiated fused silica are indicators of permanent densification that has also been observed experimentally. Published by Elsevier Science B.V

Modeling planetary interiors in laser based experiments using shockless compression

X-ray diffraction is a widely used technique for measuring the crystal structure of a compressed material. Recently, short pulse x-ray sources have been used to measure the crystal structure in-situ while a sample is being dynamically loaded. To reach the ultra high pressures that are unattainable in static experiments at temperatures lower than using shock techniques, shockless quasi-isentropic compression is required. Shockless compression has been demonstrated as a successful means of accessing high pressures. The National Ignition Facility (NIF), which will begin doing high pressure material science in 2010, it should be possible to reach over 2 TPa quasi-isentropically. This paper outlines how x-ray diffraction could be used to study the crystal structure in laser driven, shocklessly compressed targets the same way it has been used in shock compressed samples. A simulation of a shockless laser driven iron is used to generate simulated diffraction signals. And recently experimental results are presented

High-pressure, High-strain-rate Materials Effects

A 3-year LDRD-ER project to study the response of shocked materials at high pressure and high strain rate has concluded. This project involved a coordinated effort to study single crystal samples that were shock loaded by direct laser irradiation, in-situ and post-recovery measurements, and molecular dynamics and continuum modeling. Laser-based shock experiments have been conducted to study the dynamic response of materials under shock loading materials at a high strain-rate. Experiments were conducted at pressures above the published Hugoniot Elastic Limit (HEL). The residual deformation present in recovered samples was characterized by transmission electron microscopy, and the response of the shocked lattice during shock loading was measured by in-situ x-ray diffraction. Static film and x-ray streak cameras recorded x-rays diffracted from lattice planes of Cu and Si both parallel and perpendicular to the shock direction. Experiments were also conducted using a wide-angle detector to record x-rays diffracted from multiple lattice planes simultaneously. This data showed uniaxial compression of Si (100) along the shock direction and 3-dimensional compression of Cu (100). In the case of the Si diffraction, there was a multiple wave structure observed. We present results of shocked Si and Cu obtained with a new large angle diffraction diagnostic, and discuss the results in the context of detailed molecular dynamics simulations and post-processing

Variational multiscale methods to embed the macromechanical continuum formulation with fine-scale strain gradient theories

A variational basis is presented to link fine-scale theories of material behaviour with the classical, macromechanical continuum theory. The approach is based on the weak form of the linear momentum balance equations, and a separation of the weighting function and displacement fields into coarse and fine-scale components. Coarse and fine-scale weak forms are defined. The latter is used to introduce a strain gradient theory that operates at finer scales of deformation. Attention is focused upon applications requiring the enhanced physical accuracy of the fine-scale strain gradient theory, without the computational cost of discretization that spans the range from coarse to fine scales. A variationally consistent method is developed to embed the fine-scale strain gradient theory in the macromechanical formulation. The embedding is achieved by eliminating the fine-scale displacement field from the problem. Two examples demonstrate the numerical efficiency of the method, while retaining physical and mathematical properties of the fine-scale strain gradient theory. Copyright © 2003 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34538/1/727_ftp.pd