Stress Concentrations from Single-Filament Failures in Composite Materials

1969 ◽  
Vol 39 (7) ◽  
pp. 618-626 ◽  
Author(s):  
Peter Van Dyke ◽  
John M. Hedgepeth
Keyword(s):  
Matrix Material ◽  
Three Dimensional ◽  
Plastic Behavior ◽  
Two Dimensional ◽  
Failure Model ◽  
Stress Concentrations ◽  
Bond Failure ◽  
Single Filament ◽  
Concentration Problem ◽  
The Matrix

The solution of the two-dimensional, elastic, multiple-filament-failure stress concentration problem led to the treatment of three-dimensional, elastic failure models and a two-dimensional, plastic failure model where an ideally plastic behavior of the matrix material adjacent to a broken filament was assumed. Another plastic behavior is proposed wherein the bond between the broken filament and the adjacent matrix material fails completely after reaching a prescribed stress level. This failure formulation is applied to five- and seven-element-width models as well as to the infinite element case. Both the bond failure and matrix yield models are then extended to the three-dimensional cases with both square and hexagonal element configurations.

A Sequel to Technical Note 13: The Curved Tetrahedronal and Triangular Elements TEC and TRIC for the Matrix Displacement Method

1969 ◽  
Vol 73 (697) ◽  
pp. 55-65 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Computational Analysis ◽  
Three Dimensional ◽  
Technical Note ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Displacement Method ◽  
Stress Concentrations ◽  
The Past ◽  
The Matrix ◽  
Triangular Elements

It is by now well established that the computational analysis of significant problems in structural and continuum mechanics by the matrix displacement method often requires elements of higher sophistication than used in the past. This refers, in particular, to regions of steep stress gradients, which are frequently associated with marked changes in geometry, involving rapid variations of the radius of curvature. The philosophy underlying the idealisation of such configurations into finite elements was discussed in broad terms in ref. 1. It was emphasised that the so successful, constant strain, two-dimensional TRIM 3 and three-dimensional TET 4 elements do not, in general, prove the best choice. For this reason elements with a linear variation of strain like TRIM 6 and TET 10 were originally evolved and followed up with the quadratic strain elements TRIM 15, TRIA 4 (two-dimensional) and TET 20, TEA 8 (three-dimensional) of ref. 2. However, all these elements are characterised by straight edges and necessitate a polygonisation or polyhedrisation in the idealisation process. This may not be critical in many problems, but is sometimes of doubtful validity in the immediate neighbourhood of a curved boundary, where stress concentrations are most pronounced. To overcome this difficulty with a significant (local) increase of elements does not always yield the most economical and technically satisfactory solution. Moreover, there arises another inevitable shortcoming when dealing with TRIM and TET elements with a linear or quadratic variation of strain. Indeed, while TRIM 3 and TET 4 elements permit a very elegant extension into the realm of large displacements, this is not possible for the higher order TRIM and TET elements. This is simply due to the fact that TRIM 3 and TET 4 elements, by virtue of their specification, always remain straight under any magnitude of strain, but this is not so for the triangular and tetrahedron elements of higher sophistication.

Modeling of Plastic Behavior of Anisotropic Sheet Metals With Voids

2000 ◽  
Author(s):  
W. Y. Chien ◽  
J. Pan ◽  
S. C. Tang
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Yield Criterion ◽  
Plastic Anisotropy ◽  
Matrix Material ◽  
Three Dimensional ◽  
Plastic Behavior ◽  
Element Analysis ◽  
Normal Anisotropy ◽  
The Matrix

Abstract The influence of plastic anisotropy on the plastic behavior of porous ductile materials is investigated by a three-dimensional finite element analysis. A unit cell of cube containing a spherical void is modeled. The Hill quadratic anisotropic yield criterion is used to describe the matrix normal anisotropy and planar isotropy. The matrix material is assumed to be elastic perfectly plastic. Macroscopically uniform displacements are applied to the faces of the cube. The finite element computational results are compared with those based on the closed-form anisotropic Gurson yield criterion suggested in Liao et al. (Mechanics of Materials, 1997, pp. 213-226). Three fitting parameters are suggested in the closed-form yield criterion to fit the results based on the modified yield criterion to those of finite element computations.

scholarly journals Lymphocyte locomotion and attachment on two-dimensional surfaces and in three-dimensional matrices

1982 ◽  
Vol 92 (3) ◽  
pp. 747-752 ◽  
Author(s):  
WS Haston ◽  
JM Shields ◽  
PC Wilkinson
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Collagen Gels ◽  
Peripheral Lymph Node ◽  
Cellulose Esters ◽  
Peripheral Lymph ◽  
The Matrix ◽  
Identical Material ◽  
Variable Morphology ◽  
Collagen Lattices

The adhesion and locomotion of mouse peripheral lymph node lymphocytes on 2-D protein- coated substrata and in 3-D matrices were compared. Lymphocytes did not adhere to, or migrate on, 2-D substrata suck as serum- or fibronectin-coated glass. They did attach to and migrate in hydrated 3-D collagen lattices. When the collagen was dehydrated to form a 2-D surface, lymphocyte attachment to it was reduced. We propose that lymphocytes, which are poorly adhesive, are able to attach to and migrate in 3-D matrices by a nonadhesive mechanism such as the extension and expansion of pseudopodia through gaps in the matrix, which could provide purchase for movement in the absence of discrete intermolecular adhesions. This was supported by studies using serum-coated micropore filters, since lymphocytes attached to and migrated into filters with pore sizes large enough (3 or 8 mum) to allow pseudopod penetration but did not attach to filters made of an identical material (cellulose esters) but of narrow pore size (0.22 or 0.45 mum). Cinematographic studies of lymphocyte locomotion in collagen gels were also consistent with the above hypothesis, since lymphocytes showed a more variable morphology than is typically seen on plane surfaces, with formation of many small pseudopodia expanded to give a marked constriction between the cell and the pseudopod. These extensions often remained fixed with respect to the environment as the lymphocyte moved away from or past them. This suggests that the pseudopodia were inserted into gaps in the gel matrix and acted as anchorage points for locomotion.

Service quality function deployment by the C-shaped QFD 3D matrix

2018 ◽  
Vol 25 (9) ◽  
pp. 3386-3405 ◽  
Author(s):  
Maryam Hassani ◽  
Arash Shahin ◽  
Manouchehr Kheradmandnia
Keyword(s):  
Quality Function Deployment ◽  
Design Methodology ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Customer Requirements ◽  
Content Type ◽  
Process Characteristics ◽  
The Matrix ◽  
3D Matrix ◽  
Simultaneous Comparison

Purpose The purpose of this paper is to examine the application of C-shaped QFD 3D Matrix in comparing process characteristics (PC), performance aspects (PA) and customer requirements, simultaneously and to prioritize the first two sets, respectively. Design/methodology/approach A three dimensional matrix has been developed with three sets of PC, PA and customers’ requirements and C-shaped matrix has been applied for simultaneous comparison of the dimensions and prioritization of the subsets of PC and PA. The proposed approach has been examined in a post bank. Findings Findings confirm the possibility of simultaneous comparison and prioritization of the three sets of dimensions of this study in post bank services. In addition, “growth and learning” and “bilateral relationship with suppliers” had the first priorities among PA and PC, respectively. Research limitations/implications While the proposed approach has many advantages, filling the matrixes is time-consuming. Since illustrating the 3D matrix was not possible, the matrix was separated into five two-dimensional matrixes. Originality/value Compared to the studied literature, the proposed approach is practically new in the post bank services.

scholarly journals Optically transparent, high-toughness elastomer using a polyrotaxane cross-linker as a molecular pulley

2018 ◽  
Vol 4 (10) ◽  
pp. eaat7629 ◽  
Author(s):  
Hiroaki Gotoh ◽  
Chang Liu ◽  
Abu Bin Imran ◽  
Mitsuo Hara ◽  
Takahiro Seki ◽  
...  
Keyword(s):  
External Force ◽  
Matrix Material ◽  
Three Dimensional ◽  
Cross Linking ◽  
High Toughness ◽  
Dimensional Network ◽  
Cyclic Molecules ◽  
Optically Transparent ◽  
The Matrix ◽  
Special Challenge

An elastomer is a three-dimensional network with a cross-linked polymer chain that undergoes large deformation with a small external force and returns to its original state when the external force is removed. Because of this hyperelasticity, elastomers are regarded as one of the best candidates for the matrix material of soft robots. However, the comprehensive performance required of matrix materials is a special challenge because improvement of some matrix properties often causes the deterioration of others. For example, an improvement in toughness can be realized by adding a large amount of filler to an elastomer, but to the impairment of optical transparency. Therefore, to produce an elastomer exhibiting optimum properties suitable for the desired purpose, very elaborate, complicated materials are often devised. Here, we have succeeded in creating an optically transparent, easily fabricated elastomer with good extensibility and high toughness by using a polyrotaxane (PR) composed of cyclic molecules and a linear polymer as a cross-linking agent. In general, elastomers having conventional cross-linked structures are susceptible to breakage as a result of loss of extensibility at high cross-linking density. We found that the toughness of the transparent elastomer prepared using the PR cross-linking agent is enhanced along with its Young’s modulus as cross-linking density is increased.

scholarly journals Tuning cell migration: contractility as an integrator of intracellular signals from multiple cues

F1000Research ◽  
2016 ◽  
Vol 5 ◽  
pp. 1819 ◽  
Author(s):  
Francois Bordeleau ◽  
Cynthia A. Reinhart-King
Keyword(s):  
Cell Migration ◽  
Growth Factors ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Multiple Cues ◽  
Cell Contractility ◽  
Cell Matrix ◽  
Intracellular Signals ◽  
Physical Cues ◽  
The Matrix

There has been immense progress in our understanding of the factors driving cell migration in both two-dimensional and three-dimensional microenvironments over the years. However, it is becoming increasingly evident that even though most cells share many of the same signaling molecules, they rarely respond in the same way to migration cues. To add to the complexity, cells are generally exposed to multiple cues simultaneously, in the form of growth factors and/or physical cues from the matrix. Understanding the mechanisms that modulate the intracellular signals triggered by multiple cues remains a challenge. Here, we will focus on the molecular mechanism involved in modulating cell migration, with a specific focus on how cell contractility can mediate the crosstalk between signaling initiated at cell-matrix adhesions and growth factor receptors.

W1,q REGULARITY RESULTS FOR ELLIPTIC TRANSMISSION PROBLEMS ON HETEROGENEOUS POLYHEDRA

2007 ◽  
Vol 17 (04) ◽  
pp. 593-615 ◽  
Author(s):  
J. ELSCHNER ◽  
H.-C. KAISER ◽  
J. REHBERG ◽  
G. SCHMIDT
Keyword(s):  
Sobolev Space ◽  
Matrix Function ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Piecewise Constant ◽  
Transmission Problems ◽  
Corner Points ◽  
The Matrix ◽  
Regularity Results

Let ϒ be a three-dimensional Lipschitz polyhedron, and assume that the matrix function μ is piecewise constant on a polyhedral partition of ϒ. Based on regularity results for solutions to two-dimensional anisotropic transmission problems near corner points we obtain conditions on μ and the intersection angles between interfaces and ∂ϒ ensuring that the operator -∇ · μ∇ maps the Sobolev space [Formula: see text] isomorphically onto W-1,q(ϒ) for some q > 3.

Effective properties of composite materials containing voids

1993 ◽  
Vol 440 (1909) ◽  
pp. 461-473 ◽  
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Effective Properties ◽  
Young's Modulus ◽  
Matrix Material ◽  
Practical Importance ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Two Dimensional ◽  
Isotropic Composite

Recent results of theoretical and practical importance prove that the two-dimensional (in-plane) effective (average) Young’s modulus for an isotropic elastic material containing voids is independent of the Poisson’s ratio of the matrix material. This result is true regardless of the shape and morphology of the voids so long as isotropy is maintained. The present work uses this proof to obtain explicit analytical forms for the effective Young’s modulus property, forms which simplify greatly because of this characteristic. In some cases, the optimal morphology for the voids can be identified, giving the shapes of the voids, at fixed volume, that maximize the effective Young’s modulus in the two-dimensional situation. Recognizing that two-dimensional isotropy is a subset of three-dimensional transversely isotropic media, it is shown in this more general case that three of the five properties are independent of Poisson’s ratio, leaving only two that depend upon it. For three-dimensionally isotropic composite media containing voids, it is shown that a somewhat comparable situation exists whereby the three-dimensional Young’s modulus is insensitive to variations in Poisson’s ratio, v m , over the range 0 ≤ v m ≤ ½, although the same is not true for negative values of v m . This further extends the practical usefulness of the two-dimensional result to three-dimensional conditions for realistic values of v m .

Multiscale Modeling of Dynamic Characteristics of Carbon Nanotube Reinforced Nanocomposites

NANO ◽  
2016 ◽  
Vol 11 (07) ◽  
pp. 1650083 ◽  
Author(s):  
Sachin O. Gajbhiye ◽  
S. P. Singh
Keyword(s):  
Carbon Nanotube ◽  
Dynamic Characteristics ◽  
Matrix Material ◽  
Three Dimensional ◽  
Vacancy Defect ◽  
Nanocomposite Material ◽  
Phase Lag ◽  
Rate Dependent ◽  
Carbon Carbon Bond ◽  
The Matrix

A unique atomic structure of carbon nanotube unveils outstanding properties. This makes it potentially highly valued reinforcing material to strengthen composite materials. The methodology is established in this research paper to investigate the static and dynamic characteristics of the nanocomposites. Repol polypropylene H110MA is used as a matrix material along with the different percentages of single-walled carbon nanotubes (SWCNTs). A concept of representative volume element (RVE) is considered to study the various properties of the nanocomposite material. The carbon–carbon bond of nanotube is modeled using Tersoff–Brenner potential and represented by space frame element. The matrix material properties are tested in the laboratory which are further used to model it and represented by three-dimensional continuum elements. The interaction between nanotube and polymer matrix is modeled using “Lennard–Jones 6-12” potential represented by nonlinear spring elements. The effect of reinforcement, chirality, % volume of SWCNT, atomic vacancy defect and Stone–Wales defect on the properties of nanocomposite are investigated. To see the effect of reinforcement, the eigenvalues of the RVE are extracted for different boundary conditions. The viscoplastic behavior of the matrix material is considered and the rate-dependent characteristics of the nanocomposite are studied. The damping property of the nanocomposite material is also investigated based on the phase lag between stress and strain field by applying harmonic strain at different frequencies.

Matrix Representation and Prediction of Three-Dimensional Cutting Forces

1977 ◽  
Vol 99 (4) ◽  
pp. 828-834 ◽  
Author(s):  
J. A. Kirk ◽  
D. K. Anand ◽  
C. McKindra
Keyword(s):  
Cutting Forces ◽  
Metal Cutting ◽  
Present Model ◽  
Cutting Tool ◽  
Matrix Representation ◽  
Three Dimensional ◽  
Experimental Results ◽  
Analytical Models ◽  
Two Dimensional ◽  
The Matrix

Matrix geometry techniques are applied to predicting three-dimensional cutting forces. In the present model a specific cutting plane is located and two-dimensional metal cutting theory is applied. Force predictions in this plane are then matrix transformed to three orthogonal forces acting on the cutting tool. Experimental results show the matrix model accurately predicts three-dimensional cutting forces in turning of long slender workpieces. Experimental results are also compared to other analytical models described in the literature.

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