Temperature-dependent Penetration of Argon Molecules into Ultramicroporous Tunnel of a Fluoroorganic Molecular Crystal with Alteration of Its Unit Cell Size

2006 ◽  
Vol 35 (5) ◽  
pp. 504-505 ◽  
Author(s):  
Toshimasa Katagiri ◽  
Satoshi Takahashi ◽  
Koji Kawabata ◽  
Yoshiyuki Hattori ◽  
Katsumi Kaneko ◽  
...  
Keyword(s):  
Cell Size ◽  
Molecular Crystal ◽  
Unit Cell ◽  
Temperature Dependent ◽  
Unit Cell Size

Determination of Optimal Unit-Cell Size of Homogeneous Conformal Unit-Cell Lattice Structure Using Solid Shape Matching

2016 ◽  
Author(s):  
Mahmoud A. Alzahrani ◽  
Seung-Kyum Choi
Keyword(s):  
Cell Size ◽  
Solid Body ◽  
Strain Energy ◽  
Lattice Structure ◽  
Weight Ratio ◽  
Unit Cell ◽  
Optimal Size ◽  
Lattice Structures ◽  
Unit Cell Size ◽  
Unit Cells

With rapid developments and advances in additive manufacturing technology, lattice structures have gained considerable attention. Lattice structures are capable of providing parts with a high strength to weight ratio. Most work done to reduce computational complexity is concerned with determining the optimal size of each strut within the lattice unit-cells but not with the size of the unit-cell itself. The objective of this paper is to develop a method to determine the optimal unit-cell size for homogenous periodic and conformal lattice structures based on the strain energy of a given structure. The method utilizes solid body finite element analysis (FEA) of a solid counter-part with a similar shape as the desired lattice structure. The displacement vector of the lattice structure is then matched to the solid body FEA displacement results to predict the structure’s strain energy. This process significantly reduces the computational costs of determining the optimal size of the unit cell since it eliminates FEA on the actual lattice structure. Furthermore, the method can provide the measurement of relative performances from different types of unit-cells. The developed examples clearly demonstrate how we can determine the optimal size of the unit-cell based on the strain energy. Moreover, the computational cost efficacy is also clearly demonstrated through comparison with the FEA and the proposed method.

scholarly journals Influence of Unit Cell Size and Fiber Packing on the Transverse Tensile Response of Fiber Reinforced Composites

Materials ◽  
2019 ◽  
Vol 12 (16) ◽  
pp. 2565 ◽  
Author(s):  
Royan J. D’Mello ◽  
Anthony M. Waas
Keyword(s):  
Cell Size ◽  
Unit Cell ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Unit Cell Size ◽  
Tensile Response ◽  
Transverse Tensile ◽  
Macro Scale ◽  
Unit Cells

Representative volume elements (RVEs) are commonly used to compute the effective elastic properties of solid media having repeating microstructure, such as fiber reinforced composites. However, for softening materials, an RVE could be problematic due to localization of deformation. Here, we address the effects of unit cell size and fiber packing on the transverse tensile response of fiber reinforced composites in the context of integrated computational materials engineering (ICME). Finite element computations for unit cells at the microscale are performed for different sizes of unit cells with random fiber packing that preserve a fixed fiber volume fraction—these unit cells are loaded in the transverse direction under tension. Salient features of the response are analyzed to understand the effects of fiber packing and unit cell size on the details of crack path, overall strength and also the shape of the stress-strain response before failure. Provision for damage accumulation/cracking in the matrix is made possible via the Bazant-Oh crack band model. The results suggest that the choice of unit cell size is more sensitive to strength and less sensitive to stiffness, when these properties are used as homogenized inputs to macro-scale models. Unit cells of smaller size exhibit higher strength and this strength converges to a plateau as the size of the unit cell increases. In this sense, since stiffness has also converged to a plateau with an increase in unit cell size, the converged unit cell size may be thought of as an RVE. Results in support of these insights are presented in this paper.

scholarly journals Nonlinear Bloch waves and balance between hardening and softening dispersion

2018 ◽  
Vol 474 (2217) ◽  
pp. 20180173 ◽  
Author(s):  
M. I. Hussein ◽  
R. Khajehtourian
Keyword(s):  
Dispersion Relation ◽  
Cell Size ◽  
Unit Cell ◽  
Homogeneous Layer ◽  
Nonlinear Dispersion ◽  
Elastic Band ◽  
Bloch Waves ◽  
Unit Cell Size ◽  
Nonlinear Dispersion Relation ◽  
Hardening And Softening

The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals consisting of layers with alternating material properties. Considering longitudinal waves and ignoring lateral effects, the exact nonlinear dispersion relation in each homogeneous layer is first obtained and subsequently used within the transfer matrix method to derive an approximate nonlinear dispersion relation for the overall periodic medium. The result is an amplitude-dependent elastic band structure that upon verification by numerical simulations is accurate for up to an amplitude-to-unit-cell length ratio of one-eighth. The derived dispersion relation allows us to interpret the formation of spatial invariance in the wave profile as a balance between hardening and softening effects in the dispersion that emerge due to the nonlinearity and the periodicity, respectively. For example, for a wave amplitude of the order of one-eighth of the unit-cell size in a demonstrative structure, the two effects are practically in balance for wavelengths as small as roughly three times the unit-cell size.

Unit-cell size change of the thermotropic copolyester-TPA/PHQ/PEHQ under different annealing conditions

Polymer ◽  
1990 ◽  
Vol 31 (9) ◽  
pp. 1763-1767 ◽  
Author(s):  
Stephen Z.D. Cheng ◽  
Zongquan Wu ◽  
Anqiu Zhang ◽  
Ronald L. Johnson ◽  
Hak Hung Wu
Keyword(s):  
Cell Size ◽  
Unit Cell ◽  
Size Change ◽  
Unit Cell Size ◽  
Annealing Conditions

Calculation of effective material parameters by field averaging over lattices with non-negligible unit cell size

2012 ◽  
Vol 109 (4) ◽  
pp. 1007-1013 ◽  
Author(s):  
Anthony K. Amert ◽  
Victor V. Gozhenko ◽  
Keith W. Whites
Keyword(s):  
Cell Size ◽  
Unit Cell ◽  
Material Parameters ◽  
Unit Cell Size

Single scattering approximations: the domains of validity for structural analysis of protein crystals by electron diffraction

1978 ◽  
Vol 36 (1) ◽  
pp. 186-187
Author(s):  
Robert M. Glaeser ◽  
Bing K. Jap ◽  
Ming Hslu Ho
Keyword(s):  
Electron Diffraction ◽  
Cell Size ◽  
Materials Science ◽  
Single Scattering ◽  
Crystallographic Analysis ◽  
Unit Cell ◽  
Protein Crystals ◽  
Scattering Effect ◽  
Unit Cell Size ◽  
Crystal Unit Cell

Single scattering approximations (the kinematic and the weak phase object approx- imation), because of their simplicity, are perhaps the most attractive formulations for structure analysis by electron diffraction. In these approximations, the diffracted wave function is linearly related to the object potential. The validities of these approximations are, however, limited to very thin crystals at low resolution. In materials science the failure of the single scattering approximations and the impor- tance of the dynamical scattering effect have been well accepted. In biological science, the large unit cell size and the low atomic number (e.g. protein crystals) have lead some to believe that the dynamical scattering effect is insignificant for crystallographic analysis. Contrary to this belief, the number of dynamically interacting beams increases with the crystal unit cell size. It is important to note here that the dynamical scattering effect depends on the values of the excitation errors and on the magnitudes of the Fourier coefficients of the crystal potential.

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