Chiral effects cannot be described by means of the classical theories of continua. In the context of the strain gradient theory of porous elastic solids we study the deformation of a chiral cylinder subjected to torsion, extension and bending by terminal couples. This work is motivated by recent interest in using the chiral continuum as a model for some auxetic materials, bones and carbon nanotubes. The problem is reduced to the study of some two-dimensional problems. We show that the torsion of a chiral cylinder is accompanied by extension, bending, and a variation of the volume fraction field. The solution is used to investigate the deformation of a circular cylinder.
ToupinRA. Theories of elasticity with couple-stress. Arch Ration Mech Anal1964; 17: 85–112.
9.
MindlinRD. Micro-structure in linear elasticity. Arch Ration Mech Anal1964; 16: 51–78.
10.
MindlinRDEshelNN. On first strain-gradient theories in linear elasticity. Int J Solids Struct1968; 4: 109–124.
11.
NakajimaHTaneMHyunSKSekiH. Anisotropic mechanical properties of lotus-type porous metals. In: ZhaoHFleckNA (eds.) Mechanical properties of cellular materials. Berlin: Springer, 2008, 43–50.
12.
OchsnerAMurchGEde LemosMJS. Cellular and porous materials: Thermal properties simulation and prediction. Weinheim: Wiley-VCH, 2008.
13.
KohlhauserCHellmichCVitale-BrovaroneCBoccacciniARotaAEberhardsteinerJ. Ultrasonic characteristic of porous biomaterials across different frequencies. Strain2009; 45: 34–44.
14.
NunziatoJWCowinSC. A non-linear theory of elastic materials with voids. Arch Ration Mech Anal1979; 72: 175–201.
15.
CowinSCNunziatoJW. Linear elastic materials with voids. J Elasticity1983; 13: 125–147.
16.
BedfordADrumhellerDS. Theory of immiscible and structural mixtures. Int J Eng Sci1983; 21: 863–690.
17.
BirsanMAltenbachH. On the theory of porous elastic rods. Int J Solids Struct2011; 48: 910–924.
18.
GiovineP. Linear wave motions in continua with nano-pores. In: GiovineP (ed.) Wave processes in classical and new solids. New York: InTech, 2012, 62–86.
19.
BensamounSHo Ba ThoM-CLuuSGerbezzaJ-Mde BellevalJ-F. Spatial distribution of acoustic and elastic properties of femoral human cortical bone. J Biomech2004; 37: 503–510.
20.
KohlesSSRobertsJB. Linear poroelastic cancellous bone anisotropy: Trabecular solid elastic and fluid transport properties. J Biomech Eng2002; 124: 521–526.
21.
ScaliaA. A grade consistent micropolar theory of thermoelastic materials with voids. Z Angew Math Mech1992; 72: 133–140.
22.
HlavacekIHlavacekM. On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple stresses. Appl Math1969; 14: 411–427.
23.
IeşanD. On Saint-Venant’s problem. Arch Ration Mech Anal1986; 91: 363–373.
24.
IeşanD. Classical and generalized models of elastic rods. New York: Chapman & Hall, 2009.
25.
IeşanDQuintanillaR. Decay-estimates and energy bounds for porous elastic cylinders. Z Angew Math Phys1995; 46: 268–281.
26.
KahrobaiyanMHTajalliSAMovahhedyMRAkbariJAhmadianMT. Torsion of strain gradient bars. Int J Eng Sci2011; 49: 856–866.
27.
LazopoulosKALazopoulosAK. On the torsion problem of strain gradient elastic bars. Mech Res Commun2012; 45: 42–47.
