Variational formulation of a modified couple stress theory and its application to a simple shear problem

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 59, Issue 5, 2008, Pages 904-917

  Park, S K ^a   Gao, X L ^a  

^a Texas AandM University   (United States)

Author keywords

Boundary layer; Couple stress theory; Minimum total potential energy; Simple shear; Size effect; Strain gradient

Indexed keywords

ARSENIC COMPOUNDS; BOUNDARY LAYER FLOW;

BOUNDARY LAYER; COUPLE STRESS THEORY; MINIMUM TOTAL POTENTIAL ENERGY; SIMPLE SHEAR; SIZE EFFECT; STRAIN GRADIENT;

PROBLEM SOLVING;

EID: 51349157575     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-006-6073-8     Document Type: Article

References (17)

1. R. A. Toupin, Elastic materials with couple stresses. Arch. Rational Mech. Anal. 11 (1962), 385-414.
2. R. A. Toupin, Theories of elasticity with couple stress. Arch. Rational Mech. Anal. 17 (1964), 85-112.
3. R. D. Mindlin, H. F. Tiersten, Effects of couple-stresses in linear elasticity. Arch. Rational Mech. Anal. 11 (1962), 415-448.
4. R. D. Mindlin, Influence of couple-stresses on stress concentrations. Exp. Mech. 3 (1963), 1-7.
5. W. T. Kolter, Couple-stresses in the theory of elasticity. Proc. K. Ned. Akad. Wet. B 67 (1964), 17-44.
6. J. F. C. Yang, R. S. Lakes, Experimental study of micropolar and couple stress elasticity in compact bone in bending. J. Biomechanics 15 (1982), 91-98.
7. D. C. C. Lam, F. Yang, A. C. M. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51 (2003), 1477-1508.
8. F. Yang, A. C. M. Chong, D. C. C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39 (2002), 2731-2743.
9. S. K. Park, X.-L. Gao, Bernoulli-Euler beam model based on a modified couple stress theory. J. Micromech. Microeng. 16 (2006), 2355-2359.
10. X.-L. Gao, S. Mall, Variational solution for a cracked mosaic model of woven fabric com-posites. Int. J. Solids Struct. 38 (2001), 855-874.
11. R. W. Little, Elasticity. Prentice Hall, Englewood Cliffs, New Jersey 1973.
12. W. S. Slaughter, The Linearized Theory of Elasticity. Birkhäuser, Boston 2002.
13. X.-L. Gao, R. E. Rowlands, Hybrid method for stress analysis of finite three-dimensional elastic components. Int. J. Solids Struct. 37 (2000), 2727-2751.
14. L. Teneketzis Tenek, E. C. Aifantis, On some applications of gradient elasticity to composite materials. Compos. Struct. 53 (2001), 189-197.
15. S. Diebels, H. Steeb, The size effect in foams and its theoretical and numerical investigation. Proc. R. Soc. Lond. A 458 (2002), 2869-2883.
16. M. F. Horstemeyer, M. I. Baskes, V. C. Prantil, J. Philliber, S. Vonderheide, A multiscale analysis of fixed-end simple shear using molecular dynamics, crystal plasticity, and a macroscopic internal state variable theory. Modelling Simul. Mater. Sci. Eng. 11 (2003), 265-286.
17. C. Tekoglu, P. R. Onck, Size effects in the mechanical behavior of cellular materials. J. Mater. Sci. 40 (2005), 5911-5917.