Cell Method Research Articles

Effective Coefficients of Piezoelectric Fiber-Reinforced Composites

The effective coefe cients of piezoelectric e ber-reinforced composites (PFRC) have been determined through micromechanical analyzes. The method of cells (MOC) and the strength of materials (SM) approach have been employed to predict the coefe cients. A constant electric e eld is considered in the direction transverse to the e ber direction and is assumed to be the same both in the e ber and the matrix. MOC and SM predictions for the effective piezoelectric coefe cient of the PFRC assessing the actuating capability in the e ber direction are in excellent agreement. It has been found for the piezoelectric e bers considered that, when the e ber volume fraction exceeds a critical e ber volume fraction, this effective piezoelectric coefe cient becomes signie cantly larger than the corresponding coefe cient of the piezoelectric material of the e ber. The methods also show the excellent matching of the predictions of the effective elastic constants and the dielectric constant of the PFRC in the useful range of e ber volume fraction.

Crack Propagation Modeling by Remeshing Using the Cell Method (CM)

A numerical code for modeling crack prop- agation using the cell method is proposed. The Mohr- Coulomb criterion is used to compute the direction of crack propagation, and the new crack geometry is real- ized by an intra-element propagation technique. Auto- matic remeshing is then activated. Applications in Mode I and Mixed Mode are presented to illustrate the robust- ness of the implementation. keyword: Cell Method, fracture mechanics, crack propagation, automatic remeshing.

Use of the cell method for plane elastic problems in geotechnique

In the present work the use of the cell method (CM) for analysing geotechnical problems will be discussed. The essence of this method is a discrete formulation instead of a differential formulation. On the basis of this CM a computer code was developed which can be used to study the settlements related to a superficial load of an elastic multilayered soil system. With an adequate graphical support it is possible to illustrate the stress–strain state within the studied area. After an explanation of the bases of the CM an example of a simple geotechnical problem shall be presented. The problem will be limited to a two-dimensional strain state in an elastic field. The final results will be compared with the FEM analysis.

910 一方向 CFRP の時間依存挙動に関するマイクロメカニックス解析

Capability of an analytical homogenization procedure of the Aboudi generalized method of cells (MOC) to predict the off-axis time- and rate-dependent behavior of unidirectional polymer matrix composites has been elucidated. Viscous response of polymer matrix materials is described by using the Chaboche constitutive model, since it has a general structure to describe the nonlinear natures of matrix viscoplasticity. The MOC micromechanics model can favorably reproduce the rate-dependent stress-strain relationships and the time-dependent stress relaxation behavior of AS4/PEEK under off-axis conditions. Various calculations are performed for different number of the subcells of RVE and for different shape of the fiber. It is also demonstrated that the MOC micromechanics results in predictions almost comparable with those obtained by FE-based mathematical homogenization for the off-axis nonlinear behavior of unidirectional composites.

Permeability Estimation with the Method of Cells

The Method of Cells (MC) is used to predict the permeability of preforms regardless of their architecture, and to study the effect of disturbances during preform manufacturing on the permeability of the preform. Preforms are made up of bundles of fibers called fiber tows. Different types of preforms can be produced from the same fiber tow. In the MC, a repetitive unit cell is subdivided into subcells in such a way that there is only fiber tow or air in a subcell. The pressure field in each subcell is modeled as a second order polynomial of local coordinates. The coefficients of the polynomial are estimated using a set of equations that include governing equations, boundary conditions, continuity conditions and constitutive equations. Subsequently, the flow field in the subcell is determined. The pressure is averaged at the faces of the unit cell and the pressure gradient is calculated assuming a linear pressure profile across the unit cell in all three dimensions. The velocity is averaged over the unit cell volume. Finally, overall permeability values are estimated using Darcy’s Law. The geometry of the preform varies to some extent due to several effects during production or processing; or there might be some imperfections in the preform, such as improper stitches. The permeability is influenced by both of these disturbances. By varying the properties of the subcells in the model, the effect of these disturbances on the permeability can be evaluated.

Research of MOC on stress wave propagation

MOC(Method of Cell) is a new method of investigating wave propagating in material with periodic microstructure, and can reflect the effect of microstructure. In fact, by this theory, the actual composite can be transformed into a homogeneous higher order continuum with microstructure. Wave propagation in periodically bilaminated medium consisting of linearly elastic layers can be treated as a special application of this method. In this paper, it was used to simulate the dynamic response of carbon-phenolic to impulsive loading under certain boundary conditions. From the comparison between the results obtained from this method and the exact results based on propagator matrix theory, excellent agreement is achieved. Conclusion can be made that the oscillation periodicity is decided by the thickness of unit representative cell within the elastic limits of both sublayers.

Inelastic Response of a Woven Carbon/Copper Composite-Part III: Model-Experiment Correlation

This paper compares the predictions of a new micromechanics model for woven metal matrix composites with experimental results for 8-harness (8H) satin carbon/copper (C/Cu). Experimental results for this advanced woven metal matrix composite were presented in Part I of this paper (Bednarcyk and Pindera, 1999), while Part II discussed the development of the micromechanics model (Bednarcyk and Pindera, 2000). The experiments included monotonic, cyclic, and combined tension, compression, and Iosipescu shear tests. The micromechanics model is based on an embedded approach in which Aboudi's (1987) two-dimensional method of cells (MOC) is embedded within a reformulated version of Aboudi's (1995) three-dimensional generalized methods of cells (GMC-3D). In order to obtain accurate and realistic predictions, the model accounts for the effects of porosity, residual stresses, imperfect fiber/matrix bonding, and grip constraints. These effects, and the selection of the parameters, which characterize these effects, are discussed. By judiciously selecting the parameters, good qualitative and reasonable quantitative correlation is obtained between the model predictions and experiment. In particular, the unexpected trend based on matrix alloy type observed in the experimental tensile data has been correctly predicted.

Inelastic Response of a Woven Carbon/Copper Composite-Part III: Model-Experiment Correlation

This paper compares the predictions of a new micromechanics model for woven metal matrix composites with experimental results for 8-harness (8H) satin carbon/copper (C/Cu). Experimental results for this advanced woven metal matrix composite were presented in Part I of this paper (Bednarcyk and Pindera, 1999), while Part II discussed the development of the micromechanics model (Bednarcyk and Pindera, 2000). The experiments included monotonic, cyclic, and combined tension, compression, and Iosipescu shear tests. The micromechanics model is based on an embedded approach in which Aboudi's (1987) two-dimensional method of cells (MOC) is embedded within a reformulated version of Aboudi's (1995) three-dimensional generalized methods of cells (GMC-3D). In order to obtain accurate and realistic predictions, the model accounts for the effects of porosity, residual stresses, imperfect fiber/matrix bonding, and grip constraints. These effects, and the selection of the parameters, which characterize these effects, are discussed. By judiciously selecting the parameters, good qualitative and reasonable quantitative correlation is obtained between the model predictions and experiment. In particular, the unexpected trend based on matrix alloy type observed in the experimental tensile data has been correctly predicted.

Stress waves in composite materials.

The method of cells (MOC) developed by Aboudi provides a powerful means for studying the propagation of waves through systems having complicated internal cell structure [Wave Motion 9, 141 (1987)]. Laminated materials are a common example. The method can handle harmonic waves and also transient waves arising from a finite duration impulse. The method is sufficiently robust to treat impact, as we show here. Both linear and nonlinear elastic-stress-strain relations can be included. The present work generalizes the method to include viscoelastic materials (such as polymers), systems with cell structure deviating from perfect periodicity (including random), and systems simulating actual impact experiments. We test the theory by comparing our results with measurements taken from a flat-plate impact experiment. The system investigated was a bilaminate composed of unit cells of epoxy and epoxy-graphite subcells. Using known and estimated material parameters, we find that the MOC gives a reasonable representation of the data. We then address some features of the experimental data that have not yet been explained by other theoretical methods. The importance of unit cell periodicity is tested by adding a random incremental width to each unit cell. Finally, the shortcomings of the MOC caused by using a truncated series expansion for the particle displacements, and neglecting plastic flow and nonadiabatic effects are discussed.

Computer-aided microscopy in medicine: introduction to the 15 August 1987 issue of Applied Optics

New research and development opportunities and advances are evident in the multidisciplinary field of computer-aided microscopy for cell and tissue imaging and analysis. This growth applies to both the development of new and improved scientific methods as well as to the utilization of these techniques to investigate significant biomedical applications. Much of the core and supporting technology in this work involves optical and visual processes. Consequently, progress may be facilitated by stimulating the interaction between the optical scientists/engineers and the applications-oriented investigators. This 15 Aug. 1987 issue of Applied Optics presents a heterogeneous collection of papers in three sections: Scanning microscopy and related optical methodsfor cell and tissue imaging; Image cytometry/histometry systems, methods, and standards; and Biomedical applications of image cytometry and histometry. Since the purposes of this issue are to present a representative international cross-section of current research results and to provide direction and assistance to optical scientists and engineers who are interested in becoming more active in this field, this Introduction also documents relevant peer-reviewed journals and sponsoring societies, recommended didactic reading, and scheduled professional events.

Book Review: METHODS IN CELL RESEARCH, by August Ruthma G. Bell and Sons, Ltd., London, 1970, 368 p., about 524 references. Price 4 oounds, about $10

Book Review: METHODS IN CELL RESEARCH, by August Ruthma G. Bell and Sons, Ltd., London, 1970, 368 p., about 524 references. Price 4 oounds, about $10