Cylindrical indentation in micropolar elasticity

Zisis, Th.; Gourgiotis, P.A.

doi:10.1016/j.apm.2021.11.033

Cited by 7 publications

(5 citation statements)

References 61 publications

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“…5b). Our approach differed from the previous one using nanoscopic indenters to achieve high ratios of internal length scales to contact radius [43][44][45][46][47]. While we had control over lattice stiffness, twist and Poisson's ratio, we had to create a solid, connected upper surface for the indenter to load.…”

Section: Discussionmentioning

confidence: 99%

“…Further work could apply or develop Eqs. ( 8) to (18), or other 3D analysis methods [43][44][45][46][47], for off-centre contact with the unit cells, non-symmetric indenters, or anisotropic materials, where deformations in the third axis may be imbalanced. Such work could facilitate better understanding of the effect of twist during indentation, and inform the design of simpler to make, 2D extruded (orthotropic) twisting lattices.…”

Section: Discussionmentioning

confidence: 99%

“…Indentation of micropolar materials has been considered before (e.g., [43][44][45][46][47]). These works typically formulate contact pressure and radius (via local stress in 3D), to amend the equations for contact force [46].…”

Section: Introductionmentioning

confidence: 99%

“…To test this hypothesis, we develop the method of dimensional reduction to include plane stress moduli that include twist; the micropolar continuum [27,29,35] and the static variant of Willis continuum [36][37][38]. We use the established mathematical approach in the method of dimensional reduction to represent surface deformation [15,16,21,22,[43][44][45][46][47], and the material's micropolar 2D plane stress modulus to calculate contact force [15,16,21,22], then investigate a simpler 2D plane stress approximation using Willis continuum [38]. We compare these analytical results to 3D analysis methods from the literature [46], and experimental and finite element indentations of previously developed designs of mechanical metamaterials with varying amounts of twist [30].…”

Section: Introductionmentioning

confidence: 99%

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Effect of twist on indentation resistance

Duncan

Chester

Wang

et al. 2023

Materials Today Communications

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effect of twist on indentation resistance

Duncan

Chester

Wang

et al. 2023

Materials Today Communications

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“…Alternative viscoelastic material models, such as Maxwell models, or those with strain or strain rate dependent viscosity, may also better reflect foam response [95]. To use the model with some mechanical metamaterials where foam or lattice cells approach the size of the indenter, coupled micro-morphic mechanics should also be considered [107,113,114].…”

Section: Discussionmentioning

confidence: 99%

Indentation and impact response of conventional, auxetic, and shear thickening gel infused auxetic closed cell foam

Parisi

Allen

Colonna

et al. 2023

Smart Mater. Struct.

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Auxetic closed cell foams, and highly viscoelastic foams, both show potential to improve impact protection. Specifically, auxetics adapt to the shape of impacting bodies, while highly viscoelastic foams stiffen during severe impacts. So, we made auxetic closed cell foam sheets, including those that were infused with (highly viscoelastic) shear thickening gel. We then undertook comparative quasistatic and impact (drop) tests. Quasisatic tests included compression, tension and indentation. Impact tests were with a flat faced impactor at energies of 1, 3 and 5 J, and a 50 mm diameter hemisphere at 1 and 3 J. Poisson’s ratios of the foams were obtained by optical fullfield strain measurement. An analytical model was used to separate the contribution of the various measured orthotropic properties during the hemispherical impact and indentation tests. The Poisson’s ratios of the converted foams (both with and without shear thickening gel) were close to zero or marginally negative when measured through thickness. Planar values of Poisson’s ratio (measured in tension) were as low as −0.6. Through thickness Young’s moduli of the converted foams were 0.5 MPa, and planar moduli were ~12 times higher. The auxetic foams outperformed the unconverted ones during the more severe impacts, exhibiting about half the peak force during the 3 J hemispherical impacts (2.5 vs. 5 kN). The reduction in peak force was related to a measured doubling in indentation resistance for the auxetic foam. The analytical model suggests that 7 to 15% of the measured doubling in indentation resistance was due to (negative) Poisson’s ratio. Infusing the auxetic foams with shear thickening gel caused, at best, a marginal reduction in peak impact force, attributed to low and non-uniform levels of infusion.

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Frictional contact problem of a coated half plane pressed by a rigid punch with coupled stress elasticity

Çömez

El-Borgi

2023

Arch Appl Mech

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Cylindrical indentation in micropolar elasticity

Cited by 7 publications

References 61 publications

Effect of twist on indentation resistance

Effect of twist on indentation resistance

Indentation and impact response of conventional, auxetic, and shear thickening gel infused auxetic closed cell foam

Frictional contact problem of a coated half plane pressed by a rigid punch with coupled stress elasticity

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