Geometry: The leading parameter for the Poisson’s ratio of bending-dominated cellular solids

Mitschke, Holger; Schury, Fabian; Mecke, Klaus; Wein, Fabian; Stingl, Michael; Schröder‐Turk, Gerd E.

doi:10.1016/j.ijsolstr.2016.06.027

Cited by 27 publications

(23 citation statements)

References 84 publications

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“…[99][100][101][102] An important distinction is often made between bending-dominated and stretch-dominated unit cells. 82,[103][104][105][106] For the same value of the relative density, stretch-dominated lattice structures exhibit a much higher stiffness as compared to bending-dominated ones. There is a relatively simple way to determine whether a beam-based unit cell is bending-dominated or stretch-dominated.…”

Section: Relationship Between Topological Design and Quasi-static Mecmentioning

confidence: 99%

Additively manufactured porous metallic biomaterials

Zadpoor

2019

J. Mater. Chem. B

168

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Section: Relationship Between Topological Design and Quasi-static Mecmentioning

confidence: 99%

Additively manufactured porous metallic biomaterials

Zadpoor

2019

J. Mater. Chem. B

168

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“…The mathematical model of periodic frameworks is in agreement with the rigid unit mode theory used for crystalline materials ( 19 ). The bar-and-joint mechanical model is frequently adopted in the literature ( 20 – 22 ) and is gaining critical importance in structural design due to recent advances in digital manufacturing and the quest for mechanical metamaterials ( 23 , 24 ).…”

Section: Distinctive Constituents Of the Geometric Theorymentioning

confidence: 99%

Periodic Auxetics: Structure and Design

Borcea

Streinu

2017

The Quarterly Journal of Mechanics and Applied Mathematics

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SummaryMaterials science has adopted the term of auxetic behavior for structural deformations where stretching in some direction entails lateral widening, rather than lateral shrinking. Most studies, in the last three decades, have explored repetitive or cellular structures and used the notion of negative Poisson’s ratio as the hallmark of auxetic behavior. However, no general auxetic principle has been established from this perspective. In the present article, we show that a purely geometric approach to periodic auxetics is apt to identify essential characteristics of frameworks with auxetic deformations and can generate a systematic and endless series of periodic auxetic designs. The critical features refer to convexity properties expressed through families of homothetic ellipsoids.

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“…If M < 0, the structure is bending dominated; if M ≥ 0, the structure is stretch dominated. Auxetic lattices are known to be bending dominated to enable re-entrant or rolling-in mechanisms [73,74]. Therefore, mechanical analysis of truss frameworks can be useful for guiding the design process of auxetics.…”

Section: Introductionmentioning

confidence: 99%

Computational Investigation of the Effective Mechanical Behavior for 3D Pre-Buckled Auxetic Lattices

Albertini

Dirrenberger

Molotnikov

et al. 2019

Journal of Applied Mechanics

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Negative Poisson's ratio materials, or auxetics, have drawn attention for the past 30 years. The auxetic effect could lead to improved mechanical properties such as acoustic damping, indentation resistance, or crashworthiness. In this work, two 3D auxetic lattices are introduced. Auxeticity is achieved by design through pre-buckling of the lattice struts. The influence of geometrical parameters on the effective elastic properties is investigated using computational homogenization method with periodic boundary conditions. Effective Young's modulus is 3D mapped to reveal anisotropy and identify spatial orientations of interest. The effective Poisson ratio is computed for various geometric configurations to characterize auxeticity. Finally, the influence of effective elastic properties on energy dissipation under compression is explored for elastoplastic lattices with different loading directions, using finite element simulations. Results suggest that loading 3D auxetic lattices along their stiffest direction maximizes their crashworthiness.

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Geometry: The leading parameter for the Poisson’s ratio of bending-dominated cellular solids

Cited by 27 publications

References 84 publications

Additively manufactured porous metallic biomaterials

Additively manufactured porous metallic biomaterials

Periodic Auxetics: Structure and Design

Computational Investigation of the Effective Mechanical Behavior for 3D Pre-Buckled Auxetic Lattices

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