Stress and couple-stress invariance in non-centrosymmetric micropolar planar elasticity

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 467, Issue 2134, 2011, Pages 2896-2911

  Joumaa, Hady ^a   Ostoja Starzewski, Martin ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Chiral material; Composite materials; Cosserat model; Couple stress; Micropolar elasticity; Stress invariance

Indexed keywords

ELASTICITY; LINEAR TRANSFORMATIONS;

ANALYTICAL RESULTS; ANTI-PLANE; CHIRAL MATERIAL; COMPUTATIONAL PROCEDURES; COSSERAT MODEL; COUPLE-STRESS; DIRECT COUPLING; HOOKE'S LAW; IN-PLANE; LINEAR TYPES; LINEAR-SHIFT; MATERIAL MODELS; MICROPOLAR; MICROPOLAR ELASTICITY; MICROPOLAR MATERIAL; NON-CENTROSYMMETRIC; OUT-OF-PLANE; PHASE DISTRIBUTION; STRONG INVARIANCE;

MATERIALS;

EID: 80053919441     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2010.0660     Document Type: Article

References (14)

1. Cherkaev, A. V., Lurie, K. A. & Milton, G. W. 1992 Invariant properties of the stress in plane elasticity and equivalence classes of composites. Proc. R. Soc. Lond. A 438, 519-529. (doi:10.1098/rspa.1992.0123)
2. Chung, J. & Waas, A. M. 2009 The micropolar elasticity constants of circular cell honeycombs. Proc. R. Soc. A 465, 25-39. (doi:10.1098/rspa.2008. 0225)
3. Dundurs, J. & Markenscoff, X. 1993 Invariance of stress under a change of elastic compliances. Proc. R. Soc. Lond. A 443, 289-300. (doi:10.1098/rspa.1993.0146)
4. Hu, G. K. & Weng, G. J. 2001 A new derivative on the shift property of effective elastic compliances for planar and three-dimensional composites. Proc. R. Soc. Lond. A 457, 1675-1684. (doi:10.1098/rspa.2001.0783)
5. Jasiuk, I. 2009 Stress invariance and exact relations in the mechanics of composite materials: extensions of the CLM result: a review. Mech. Mater. 41, 394-404. (doi:10.1016/j.mechmat. 2009.01.001)
6. Jasiuk, I. & Ostoja-Starzewski, M. 2003 On the reduction of constants in planar Cosserat elasticity with eigenstrains and eigencurvatures. J. Therm. Stresses 26, 1221-1228. (doi:10.1080/714050882)
7. Milton, G. W. 2002 The theory of composites, pp. 59-73. Cambridge, UK: Cambridge University Press.
8. Mora, R. & Waas, A. M. 2000 Measurement of the Cosserat constant of circular-cell polycarbonate honeycomb. Phil. Mag. A 80, 1699-1713. (doi:10.1080/01418610008212145) (Pubitemid 35393481)
9. Moran, B. & Gosz, M. 1994 Stress invariance in plane anisotropic elasticity. Model. Simul. Mater. Sci. Eng. 2, 677-688. (doi:10.1088/0965-0393/2/ 3A/017)
10. Norris, A. N. 1999 Stress invariance and redundant moduli in three dimensional elasticity. Proc. R. Soc. Lond. A 455, 4097-4116. (doi:10.1098/rspa.1999.0492)
11. Nowacki, W. 1986 Theory of asymmetric elasticity. Oxford, UK: Pergamon Press.
12. Ostoja-Starzewski, M. 2008 Microstructural randomness and scaling in mechanics of materials. Boca Raton, FL: Chapman and Hall/CRC Press.
13. Ostoja-Starzewski, M. & Jasiuk, I. 1995 Stress invariance in planar Cosserat elasticity. Proc. R. Soc. Lond. A 451, 453-470. (doi:10.1098/rspa.1995. 0136)
14. Thorpe, M. F. & Jasiuk, I. 1992 New results in the theory of elasticity for two-dimensional composites. Proc. R. Soc. Lond. A 438, 531-544. (doi:10.1098/rspa.1992.0124)