Torsion of Chiral Porous Elastic Beams
Source abstract
Abstract
This paper is concerned with the equilibrium theory of chiral porous elastic solids. We study the problem of torsion, bending and extension of chiral cylinders. First, it is shown that the solution can be found as a vector field which has the property that its partial derivative with respect to axial coordinate corresponds to a rigid deformation. Then, we reduce the problem to the study of some two-dimensional problems. With the help of these results we can investigate the bending by terminal couples and the problems of extension and torsion. The solution is used to study the torsion of a chiral circular cylinder.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Elasticity and Material Modeling · Thermoelastic and Magnetoelastic Phenomena · Advanced Mathematical Modeling in Engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (23)
Show source-provided references
1. Lakes, R.: Elastic and viscoelastic behaviour of chiral materials. Int. J. Mech. Sci. 43, 1579–1589 (2001)10.1016/S0020-7403(00)00100-4 ↗
2. Lakes, R.S.: Dynamical study of couple stress effects in human compact bone. J. Biomech. Eng. 104, 6–11 (1982)10.1115/1.3138308 ↗
3. Lakes, R.S., Benedict, R.L.: Noncentrosymmetry in micropolar elasticity. Int. J. Eng. Sci. 29, 1161–1167 (1982)10.1016/0020-7225(82)90096-9 ↗
4. Lakes, R.S., Yoon, H.S., Katz, J.L.: Slow compressional wave propagation in wet human and bovine cortical bone. Science 200, 513–515 (1983)10.1126/science.6836296 ↗
5. Park, H.C., Lakes, R.S.: Cosserat micromechanics of human bone: strain redistribution by a hydratation-sensitive constituent. J. Biomech. 19, 1038–1040 (1986)10.1016/0021-9290(86)90015-1 ↗
6. Lakes, R.S.: Elastic freedom in cellular solids and composite materials. In: Golden, K., Grimmert, G., James, R., Milton, G., Sen, P. (eds.) Mathematics of Multiscale Materials, IMA, vol. 99, pp. 129–153. Springer, Berlin (1988)10.1007/978-1-4612-1728-2_9 ↗
7. Prall, D., Lakes, R.S.: Properties of a chiral honeycomb with a Poisson’s ratio-1. Int. J. Mech. Sci. 39, 305–314 (1997)10.1016/S0020-7403(96)00025-2 ↗
8. Ha, C.S., Plesha, M.E., Lakes, R.S.: Chiral three dimensional lattices with tunable Poissons ratio. Smart Mater. Struct. 25, 054005 (2016)10.1088/0964-1726/25/5/054005 ↗
9. Dyszlewicz, J.: Micropolar Theory of Elasticity. Springer, New York (2004)10.1007/978-3-540-45286-7 ↗
10. Natroshvili, D., Stratis, I.G.: Mathematical problems of the theory of elasticity of chiral materials for Lipschitz domains. Math. Methods Appl. Sci. 29, 445–478 (2005)10.1002/mma.696 ↗
11. Chandraseker, K., Mukherjee, S., Paci, J.T., Schatz, G.C.: An atomistic continuum Cosserat rod model of carbon nanotubes. J. Mech. Phys. Solids 57, 932–958 (2009)10.1016/j.jmps.2009.02.005 ↗
12. Nunziato, J.W., Cowin, S.C.: A non-linear theory of elastic materials with voids. Arch. Ration. Mech. Anal. 72, 175–201 (1979)10.1007/BF00249363 ↗
13. Cowin, S.C., Nunziato, J.W.: Linear elastic materials with voids. J. Elast. 13, 125–147 (1983)10.1007/BF00041230 ↗
14. Eringen, A.C.: Microcontinuum Field Theories I: Foundations and Solids. Springer, Heidelberg (1999)10.1007/978-1-4612-0555-5 ↗
15. Kohles, S.S., Roberts, J.B.: Linear poroelastic cancellous bone anisotropy: trabecular solid elastic and fluid transport properties. J. Biomech. Eng. 124, 521–526 (2002)10.1115/1.1503374 ↗
16. Fatemi, J., van Keulen, F., Onck, P.R.: Generalized continuum theories: applications to stress analysis of bone. Meccanica 37, 385–396 (2002)10.1023/A:1020839805384 ↗
17. DeCicco, S., Nappa, L.: Torsion and flexure of microstretch elastic circular cylinders. Int. J. Eng. Sci. 35, 573–583 (1997)10.1016/S0020-7225(96)00110-3 ↗
18. Scalia, A.: Extension, bending and torsion of anisotropic microstretch elastic cylinders. Math. Mech. Solids 5, 31–40 (2000)10.1177/108128650000500103 ↗
19. Ieşan, D., Pompei, A.: On the equilibrium theory of microstretch elastic solids. Int. J. Eng. Sci. 33, 399–410 (1995)10.1016/0020-7225(94)00067-T ↗
20. Ieşan, D.: On Saint-Venants problem. Arch. Ration. Mech. Anal. 91, 363–373 (1986)10.1007/BF00282340 ↗
21. Hlavacek, I., Hlavacek, M.: On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. Apl. Mat. 14, 411–427 (1969)10.21136/AM.1969.103249 ↗
22. Fichera, G.: Existence theorems in elasticity. In: Truesdel, C. (ed.) Handbuch der Physik, vol. VI a/2. Springer, Berlin (1972)
23. Ieşan, D.: Classical and Generalized Models of Elastic Rods. Chapman & Hall/CRC Press, London/New York (2009)