A nonlinear negative stiffness metamaterial unit cell and small-on-large multiscale material model

Advanced woven fabrics can provide a wide range of mechanical properties since the yarns can be arranged in different architectural patterns thus allowing the fabric structure to be tuned based on the specific needs. This adjustable nature makes them an attractive material choice for applications where versatility is highly desired. Hence, there is an increasing interest in woven fabrics in the recent years. They have been used in various applications such as deployable structures, protective garments, medical scaffolds and composites. With the increased interest, there is a need for efficient and accurate computational tools to investigate the mechanical behavior and deformation of woven fabrics for specific applications. Although there are several computational models in the literature that can model uniaxial and biaxial behavior of woven fabrics, there are not any commonly accepted material models for woven fabrics due to the complex interaction of trellising and deformation. Here, we propose an easy to implement constitutive material model based on a mesoscale unit cell of the woven fabrics. The proposed model utilizes the two prominent deformation mechanisms affecting the mechanical response at the mesoscale level: (1) Yarn stretching, and (2) shearing. These mesoscale mechanisms are mechanistically implemented within an unit cell by using truss and rotational springs to generate the mechanical response of the woven fabric. The yarns’ nonlinear mechanical behavior is modeled with non-linear trusses and assumed to be pin-jointed at the center of the unit cell. The truss elements are allowed to rotate at the pin-joint reproducing the yarns’ relative rotational motion during shearing. The fabric’s shear resistance involves two components: yarn-to-yarn relative rotation/sliding and yarn locking due to the yarn transverse compression. These components of the fabric shear resistance are modeled as a non-linear rotational spring located at the pin-joint which generates a moment resisting the shear deformation. The developed forces and moments from the trusses and rotational spring within the unit cell structure are then used to determine the continuum stress state of the material point. The material properties and parameters defined in the proposed model are easy to obtain from uniaxial tensile and shear tests on fabrics. To validate the material model, plain weave Kevlar KM2 fabric is modeled by replicating the standard uniaxial tensile and bias extension tests. The results obtained show that the material model provides a good description of the in-plane deformation and mechanical response.

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Hierarchical Design of Composite Materials With Negative Stiffness Inclusions Using a Bayesian Network Classifier

Volume 3A: 39th Design Automation Conference ◽

10.1115/detc2013-13128 ◽

2013 ◽

Cited By ~ 2

Author(s):

Jordan Matthews ◽

Timothy Klatt ◽

Carolyn C. Seepersad ◽

Michael Haberman ◽

David Shahan

Keyword(s):

Composite Materials ◽

Bayesian Network ◽

Hierarchical Modeling ◽

Effective Properties ◽

Material Model ◽

Negative Stiffness ◽

Mechanical Stiffness ◽

High Loss ◽

High Stiffness ◽

Bayesian Network Classifiers

Recent research in the field of composite materials has shown that it is theoretically possible to produce composite materials with macroscopic mechanical stiffness and loss properties that surpass those of conventional composites. This research explores the possibility of designing and fabricating these composite materials by embedding small volume fractions of negative stiffness inclusions in a continuous host material. Achieving high stiffness and loss from these materials by design, however, is a nontrivial task. This paper presents a hierarchical multiscale material model for these materials, coupled with a set-based, multilevel design approach based on Bayesian network classifiers. Bayesian network classifiers are used to map promising regions of the design space at each hierarchical modeling level, and then the maps are intersected to identify sets of multilevel or multiscale solutions that are likely to provide desirable system performance. Length scales range from the behavior of the structured microscale negative stiffness inclusions to the effective properties of mesoscale composite materials to the performance of an illustrative macroscale component — a vibrating beam coated with the high stiffness, high loss composite material.

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High-resolution structure determination by ALCHEMI

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100074707 ◽

1983 ◽

Vol 41 ◽

pp. 178-181 ◽

Cited By ~ 1

Author(s):

Peter G. Self ◽

Peter R. Buseck

Keyword(s):

Site Occupancy ◽

Real Space ◽

Unit Cell ◽

Bragg Angle ◽

Electron Current ◽

High Resolution Structure ◽

Beam Incident ◽

Crystallographic Planes ◽

Electron Beam Incident ◽

Resolution Structure

ALCHEMI (Atom Location by CHanneling Enhanced Microanalysis) enables the site occupancy of atoms in single crystals to be determined. In this article the fundamentals of the method for both EDS and EELS will be discussed. Unlike HRTEM, ALCHEMI does not place stringent resolution requirements on the microscope and, because EDS clearly distinguishes between elements of similar atomic number, it can offer some advantages over HRTEM. It does however, place certain constraints on the crystal. These constraints are: a) the sites of interest must lie on alternate crystallographic planes, b) the projected charge density on the alternate planes must be significantly different, and c) there must be at least one atomic species that lies solely on one of the planes.An electron beam incident on a crystal undergoes elastic scattering; in reciprocal space this is seen as a diffraction pattern and in real space this is a modulation of the electron current across the unit cell. When diffraction is strong (i.e., when the crystal is oriented near to the Bragg angle of a low-order reflection) the electron current at one point in the unit cell will differ significantly from that at another point.

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The External Shape of Human γ GI Immunoglobulin from Crystal Sections

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010006619x ◽

1971 ◽

Vol 29 ◽

pp. 428-429

Author(s):

L. W. Labaw

Keyword(s):

Molecular Weight ◽

Sodium Phosphate ◽

Osmium Tetroxide ◽

Unit Cell ◽

Monoclinic Space Group ◽

X Ray ◽

Large Molecular Weight ◽

Cell Dimensions ◽

Unit Cell Dimensions ◽

Crystallographic Axes

Crystals of a human γGl immunoglobulin have the external morphology of diamond shaped prisms. X-ray studies have shown them to be monoclinic, space group C2, with 2 molecules per unit cell. The unit cell dimensions are a = 194.1, b = 91.7, c = 51.6Å, 8 = 102°. The relatively large molecular weight of 151,000 and these unit cell dimensions made this a promising crystal to study in the EM.Crystals similar to those used in the x-ray studies were fixed at 5°C for three weeks in a solution of mother liquor containing 5 x 10-5M sodium phosphate, pH 7.0, and 0.03% glutaraldehyde. They were postfixed with 1% osmium tetroxide for 15 min. and embedded in Maraglas the usual way. Sections were cut perpendicular to the three crystallographic axes. Such a section cut with its plane perpendicular to the z direction is shown in Fig. 1.This projection of the crystal in the z direction shows periodicities in at least four different directions but these are only seen clearly by sighting obliquely along the micrograph.

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The orientation of sickle hemoglobin fibers within fascicles

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100104066 ◽

1988 ◽

Vol 46 ◽

pp. 400-401

Author(s):

Christopher A. Miller ◽

Bridget Carragher ◽

William A. McDade ◽

Robert Josephs

Keyword(s):

Sickle Cell ◽

Sickle Cell Anemia ◽

Relative Orientation ◽

Unit Cell ◽

Red Cell ◽

High Ph ◽

Sickle Hemoglobin ◽

Polar Crystal ◽

Helical Configuration

Highly ordered bundles of deoxyhemoglobin S (HbS) fibers, termed fascicles, are intermediates in the high pH crystallization pathway of HbS. These fibers consist of 7 Wishner-Love double strands in a helical configuration. Since each double strand has a polarity, the odd number of double strands in the fiber imparts a net polarity to the structure. HbS crystals have a unit cell containing two double strands, one of each polarity, resulting in a net polarity of zero. Therefore a rearrangement of the double strands must occur to form a non-polar crystal from the polar fibers. To determine the role of fascicles as an intermediate in the crystallization pathway it is important to understand the relative orientation of fibers within fascicles. Furthermore, an understanding of fascicle structure may have implications for the design of potential sickling inhibitors, since it is bundles of fibers which cause the red cell distortion responsible for the vaso-occlusive complications characteristic of sickle cell anemia.

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Kinematical and Dynamical CBED Pattern Models: Increasing the Accuracy of the Unit-Cell Parameter Measurements Based on CBED Patterns

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100136301 ◽

1990 ◽

Vol 48 (2) ◽

pp. 540-541

Author(s):

I.N. Yadhikov ◽

S.K. Maksimov

Keyword(s):

Reciprocal Lattice ◽

Unit Cell ◽

Reciprocal Lattice Vector ◽

Unit Cell Parameters ◽

Lattice Vector ◽

Cell Parameters ◽

Accuracy Of Measurements ◽

The Difference ◽

Image Position ◽

Convergent Beam

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.

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Structure Information From Electron Diffraction Intensities

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100136180 ◽

1990 ◽

Vol 48 (2) ◽

pp. 516-517

Author(s):

J. Gjønnes ◽

N. Bøe ◽

K. Gjønnes

Keyword(s):

Computational Effort ◽

Unit Cell ◽

Small Unit ◽

Structure Information ◽

Dispersion Surface ◽

Integrated Intensity ◽

The One ◽

Image Position ◽

Convergent Beam ◽

Beam Patterns

Structure information of high precision can be extracted from intentsity details in convergent beam patterns like the one reproduced in Fig 1. From low order reflections for small unit cell crystals,bonding charges, ionicities and atomic parameters can be derived, (Zuo, Spence and O’Keefe, 1988; Zuo, Spence and Høier 1989; Gjønnes, Matsuhata and Taftø, 1989) , but extension to larger unit cell ma seem difficult. The disks must then be reduced in order to avoid overlap calculations will become more complex and intensity features often less distinct Several avenues may be then explored: increased computational effort in order to handle the necessary many-parameter dynamical calculations; use of zone axis intensities at symmetry positions within the CBED disks, as in Figure 2 measurement of integrated intensity across K-line segments. In the last case measurable quantities which are well defined also from a theoretical viewpoint can be related to a two-beam like expression for the intensity profile:With as an effective Fourier potential equated to a gap at the dispersion surface, this intensity can be integrated across the line, with kinematical and dynamical limits proportional to and at low and high thickness respctively (Blackman, 1939).

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The crystal structure of eugaAl

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100131899 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1452-1453

Author(s):

H. Brigitte Krause ◽

Yonglin Qian

Keyword(s):

Crystal Structure ◽

Electron Microscope ◽

Zone Axis ◽

Unit Cell ◽

Polycrystalline Specimen ◽

Lattice Constants

A polycrystalline specimen of nominal formula EuGaAl with unknown crystal structure was investigated by various electron microscope techniques; EDS-, SED-, and CBED data were taken on a Philips 400 electron microscope operated at 100kV, HREM data on a Hitachi 9000 microscope operated at 300kV. The EDS data confirmed the composition for the bulk of the material but, in addition, revealed particles with other fractions of the elements. Only the EuGaAl particles were further investigated. The unit cell was determined to be orthorhombic with a ratio: a/b=0.969(2) , a/c=0.234(2) and b/c=0.234(2). The lattice constants are a=4.54(5)Ȧ, b=4.68Ȧ and c=19.97(20)Ȧ. Based on systematic extinctions for hkl reflections with h+l=2n+l, the unit cell was found to be b-centered. CBED patterns of the [001], [100], and [010] zone axes are shown in Fig. 1. The zone axis patterns are in agreement with the above stated data except for diffused (2m+l,2n+l,0)- reflections, not compatible with the above stated systematic absences. But these occurred only occasionally in conjunction with a complicated noncommensurate superlattice pattern.

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