Elastic Moduli of Two Dimensional Materials With Polygonal and Elliptical Holes

1994 ◽  
Vol 47 (1S) ◽  
pp. S18-S28 ◽  
Author(s):  
I. Jasiuk ◽  
J. Chen ◽  
M. F. Thorpe
Keyword(s):  
Elastic Constants ◽  
Conformal Transformation ◽  
Elastic Moduli ◽  
Far Field ◽  
Effective Elastic Moduli ◽  
Two Dimensional ◽  
Effective Elastic Constants ◽  
Two Dimensional Materials ◽  
Elliptical Holes ◽  
General Relations

We study the effective elastic moduli of two-dimensional composite materials containing polygonal holes. In the analysis we use a complex variable method of elasticity involving a conformal transformation. Then we take a far field result and derive the effective elastic constants of composites with a dilute concentration of polygonal holes. In the discussion we use the recently-stated Cherkaev-Lurie-Milton theorem, which gives general relations between the effective elastic constants of two-dimensional composites. We also discuss known results for elliptical holes in the context of the present work.

Effective Elastic Moduli of Composite Materials: Reduced Parameter Dependence

1997 ◽  
Vol 50 (11S) ◽  
pp. S39-S43 ◽  
Author(s):  
John Dundurs ◽  
Iwona Jasiuk
Keyword(s):  
Composite Materials ◽  
Elastic Constants ◽  
Elastic Moduli ◽  
Plane Elasticity ◽  
Parameter Dependence ◽  
Effective Elastic Moduli ◽  
Independent Variables ◽  
Effective Elastic Constants

In this paper, we focus on the effective elastic constants of composite materials and pay attention to the possibility of reducing the number of independent variables. Surprisingly, this important issue has hardly been explored before. In our analysis, we rely on a new result in plane elasticity due to Cherkaev, Lurie, and Milton (1992), and use Dundurs constants (Dundurs, 1967, 1969). As an example, we consider a result for the effective elastic moduli of a composite containing a dilute concentration of perfectly-bonded circular inclusions.

scholarly journals Evaluation of Effective Elastic Properties of Nitride NWs/Polymer Composite Materials Using Laser-Generated Surface Acoustic Waves

2018 ◽  
Vol 8 (11) ◽  
pp. 2319 ◽  
Author(s):  
Evgeny Glushkov ◽  
Natalia Glushkova ◽  
Bernard Bonello ◽  
Lu Lu ◽  
Eric Charron ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Composite Materials ◽  
Elastic Constants ◽  
Acoustic Waves ◽  
Composite Structures ◽  
Elastic Moduli ◽  
Surface Acoustic Waves ◽  
Dispersion Curves ◽  
Effective Elastic Moduli ◽  
Asymptotic Representations

In this paper we demonstrate a high potential of transient grating method to study the behavior of surface acoustic waves in nanowires-based composite structures. The investigation of dispersion curves is done by adjusting the calculated dispersion curves to the experimental results. The wave propagation is simulated using the explicit integral and asymptotic representations for laser-generated surface acoustic waves in layered anisotropic waveguides. The analysis of the behavior permits to determine all elastic constants and effective elastic moduli of constituent materials, which is important both for technological applications of these materials and for basic scientific studies of their physical properties.

scholarly journals Effective elastic moduli of two-dimensional solids with multiple cracks

1998 ◽  
Vol 41 (10) ◽  
pp. 1114-1120 ◽  
Author(s):  
Shige Zhan ◽  
Ziqiang Wang ◽  
Xueli Han
Keyword(s):  
Elastic Moduli ◽  
Multiple Cracks ◽  
Effective Elastic Moduli ◽  
Two Dimensional

scholarly journals Effect of the Grain Shape on the Elastic Constants of Polycrystalline Materials

1996 ◽  
Vol 28 (1-2) ◽  
pp. 17-33 ◽  
Author(s):  
H. Kiewel ◽  
H. J. Bunge ◽  
L. Fritsche
Keyword(s):  
Boundary Value Problem ◽  
Coordination Number ◽  
Elastic Constants ◽  
Elastic Moduli ◽  
Grain Shape ◽  
Polycrystalline Materials ◽  
Stress And Strain ◽  
Effective Elastic Moduli ◽  
Real Material ◽  
Effective Constants

We examine the influence of the grain shape on the effective elastic moduli of polycrystalline materials. For that purpose the real material is simulated by a cluster of Wigner-Seitz cells. For clarity each aggregate consists of grains with only one type of shape. Therefore we can classify each cluster by the coordination number of its grains. To determine the elastic moduli a homogeneous deformation is subjected to the surface of the cluster. The solution of this boundary value problem yields the average stress and strain governing inside the material whose interconnection by Hooke's law leads to the sought-for effective constants.The most important result is that with increasing coordination number the elastic moduli decrease.

Effective Elastic Moduli of Two-Dimensional Brittle Solids With Interacting Microcracks, Part I: Basic Formulations

1994 ◽  
Vol 61 (2) ◽  
pp. 349-357 ◽  
Author(s):  
J. W. Ju ◽  
Tsung-Muh Chen
Keyword(s):  
Elastic Moduli ◽  
Effective Elastic Moduli ◽  
Two Dimensional ◽  
Damage Models ◽  
Brittle Solids ◽  
Averaged Equations ◽  
Approximate Analytical Solutions ◽  
Special Cases ◽  
Microcrack Growth ◽  
Microcrack Interaction

Statistical micromechanical formulations are presented to investigate effective elastic moduli of two-dimensional brittle solids with interacting slit microcracks. The macroscopic stress-strain relations of elastic solids with interacting microcracks are micromechanically derived by taking the ensemble average over all possible realizations which feature the same material microstructural geometry, characteristics, and loading conditions. Approximate analytical solutions of a two-microcrack interaction problem are introduced to account for microcrack interaction among many randomly oriented and located microcracks. The overall elastic-damage compliances of microcrack-weakened brittle solids under uniaxial and biaxial loads are also derived. Therefore, stationary statistical micromechanical formulation is completed. Moreover, some special cases are investigated by using the proposed framework. At variance with existing phenomenological continuum damage models, the proposed framework does not employ any fitted “material parameters. ” “Cleavage 1” microcrack growth and “evolutionary damage models” within the proposed context will be presented in Part II of this series. It is emphasized that microstructural statistical informations are already embedded in the proposed ensemble-averaged equations and, therefore, no Monte Carlo simulations are needed.

Redox-Active Approach Towards New Magnetic And Conductive Two-Dimensional Materials

2018 ◽  
Author(s):  
Penny Perlepe ◽  
Rodolphe Clérac ◽  
Itziar Oyarzabal ◽  
Corine Mathonière
Keyword(s):  
Two Dimensional ◽  
Active Approach ◽  
Redox Active ◽  
Two Dimensional Materials
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