On Gradient Elasticity and Discrete Peridynamics with Applications to Beams and Plates

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Abstract:

In this paper two different nonlinear elasticity theories that account for (a) geometric nonlinearityand (b) microstructure-dependent size effects are revisited to establish the connection betweenthe two theories. The first theory is based on modified couple stress theory of Yang et al. [1]and the second one is based on Srinivasa–Reddy gradient elasticity theory [2]. The modified couplestress theory includes a material length scale parameter that can capture the size effect in a material.The gradient elasticity theory was developed for finitely deforming hyperelastic cosserat continuum,and it is a generalization of small deformation couple stress theories. The Srinivasa–Reddy theorycontains, as a special case, the first one. These two theories are used to derive the governing equationsof beams and plates. In addition, a discrete peridynamics idea as an alternative to the conventionalperidynamics is also presented.

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145-154

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August 2013

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[1] F. Yang, A. C. M. Chong, D. C. C. Lam, and P. Tong: Int. J. Solids Struct., Vol. 39 (2002), p.2731.

Google Scholar

[2] A. R. Srinivasa and J. N. Reddy: J. Mech. Phys. Solids, Vol. Vol. 61, No. 3 (2013), p.873.

Google Scholar

[3] D. C. C. Lam, F. Yang, A. C. M. Chong, J. Wang, and P. Tong: J. Mech. Phys. Solids, Vol. 51 (2003), p.1477.

Google Scholar

[4] A. W. McFarland and J. S. Colton: J. Micromech. Microeng., Vol. 15 (2005), p.1060.

Google Scholar

[5] R. D. Mindlin: Experimental Mechanics Vol. 3, No. 1 (1963), p.1.

Google Scholar

[6] A. E. Green, P. M. Naghdi, and R. S. Rivlin: Int. J. Engng. Sci., Vol. 2, No. 6 (1965), p.611.

Google Scholar

[7] A. E. Green and P. M. Nagdi: Proc. Royal Soc. London Series A: Math. Phys. Sci., Vol. 448, No. 1934 (1995), p.357.

Google Scholar

[8] W. T. Koiter: Proc. K. Ned. Akad. Wet. B, Vol. 67 (1964) p.17.

Google Scholar

[9] S. Papargyri-Beskou, K. G. Tsepoura, D. Polyzos, and D. E. Beskos: Int. J. Solids Struct., Vol. 40 (2003), p.385.

DOI: 10.1016/j.ijsolstr.2005.02.022

Google Scholar

[10] J. F. C. Yang and R. S. Lakes: J. Biomech., Vol. 15 (1982), p.91.

Google Scholar

[11] R. Maranganti and P. Sharma: J. Mech. Phys. Solids, Vol. 55 (2007), p.1823.

Google Scholar

[12] S. K. Park and X.-L. Gao: J. Micromech. Microengng., Vol. 16 (2006), p.2355.

Google Scholar

[13] S. K. Park and X.-L. Gao: Z. angew. Math. Phys., Vol. 59 (2008), p.904.

Google Scholar

[14] H. M. Ma, X. -L. Gao, and J. N. Reddy: J. Mech. Phys. Solids, Vol. 56 (2008), p.3379.

Google Scholar

[15] H. M. Ma, X. -L. Gao, and J. N. Reddy: Acta Mech., Vol. 220 (2011), p.217.

Google Scholar

[16] J. N. Reddy: J. Mech. Phys. Solids, Vol. 59 (2011), p.2382.

Google Scholar

[17] W. Xia, L. Wang, and L. Yin: Int. J. Engng. Sci., Vol. 48 (2010), p.2044.

Google Scholar

[18] L. L. Ke and Y. S. Wang: Compos. Struct., Vol. 93 (2011), p.342.

Google Scholar

[19] J. N. Reddy and J. Kim: Compos. Struct., Vol. 94 (2012), p.1128.

Google Scholar

[20] A. Arbind and J. N. Reddy: Compos. Struct., Vol. 98 (2013), p.272.

Google Scholar

[21] J. Kim and J. N. Reddy: Compos. Struct., Vol. 103 (2013), p.86.

Google Scholar

[22] J. N. Reddy: Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons, New York (2002).

Google Scholar

[23] S. A. Silling: J. Mech. Phys. Solids, Vol. 48 (2000), p.175.

Google Scholar

[24] S. A. Silling, M. Zimmermann, and R. Abeyaratne: J. Elasticity Vol. 73 (2003), p.173.

Google Scholar

[25] S. A. Silling and E. Askari: Comput. & Struct., Vol. 83 (2005), p.1526.

Google Scholar

[26] S. A. Silling and F. Bobaru: Int. J. Non-Linear Mech., Vol. 40 (2005), p.395.

Google Scholar

[27] J. N. Reddy: An Introduction to the Finite Element Method, McGraw-Hill, New York (2006)

Google Scholar