TY - JOUR
T1 - Cavities vis-a-vis rigid inclusions
T2 - Elastic moduli of materials with polygonal inclusions
AU - Jasiuk, Iwona
N1 - Funding Information:
Acknowledgements--We would like to thank Professors M. Ostoja-Starzewski and M. F. Thorpe for useful discussions and W. Wang for the help in preparing the plots. We would also like to thank Professors X. Markenscoffand M. V. Paukshto for bringing to the author's attention Mikhlin's result for the Cosserat spectrum at q = 0. This research was supported by the Composite Materials and Structures Center at Michigan State University through the Research Excellence Fund from the State of Michigan and by the Institute for Mechanics and Materials during the author's visit at the University of California in San Diego.
PY - 1995/2
Y1 - 1995/2
N2 - In this paper we explore the correspondence between rigid inclusions and cavities [Dundurs(1989, J. Appl. Mech. 56, 786-790)] as applied to the effective elastic moduli of materials with polygonal rigid inclusions and cavities. In the analysis we use a complex variable method of elasticity and a conformal transformation to solve for the stress field due to a single rigid inclusion. Then we use a far field approach to obtain the effective elastic constants of composites with a dilute concentration of rigid polygonal inclusions. By employing the Dundurs correspondence we can automatically obtain the result for the effective elastic moduli of materials with cavities. Finally, we use effective medium theories to predict the elastic moduli of materials containing a finite concentration of inclusions.
AB - In this paper we explore the correspondence between rigid inclusions and cavities [Dundurs(1989, J. Appl. Mech. 56, 786-790)] as applied to the effective elastic moduli of materials with polygonal rigid inclusions and cavities. In the analysis we use a complex variable method of elasticity and a conformal transformation to solve for the stress field due to a single rigid inclusion. Then we use a far field approach to obtain the effective elastic constants of composites with a dilute concentration of rigid polygonal inclusions. By employing the Dundurs correspondence we can automatically obtain the result for the effective elastic moduli of materials with cavities. Finally, we use effective medium theories to predict the elastic moduli of materials containing a finite concentration of inclusions.
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U2 - 10.1016/0020-7683(94)00119-H
DO - 10.1016/0020-7683(94)00119-H
M3 - Article
AN - SCOPUS:0029251210
SN - 0020-7683
VL - 32
SP - 407
EP - 422
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
IS - 3-4
ER -