A way to hypo-elastic artificial materials without a strain potential and displaying flutter instability

Bordiga, G.; Bigoni, Davide

doi:10.1016/j.jmps.2021.104665

Cited by 8 publications

(7 citation statements)

References 33 publications

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“…Again similarly to nonassociative elastoplasticity, the acoustic tensor (4.4) can have two complex conjugate eigenvalues, defining flutter instability in a continuum. Indeed this instability was found in the homogenized response of the non-Hermitian elastic material obtained by Bordiga et al [201] through the homogenization of a grid of elastic rods, figure 8a. In this way, a formal link has been discovered between structural flutter and its occurrence in a continuum.…”

Section: (D) Metamaterials and Non-hermitian Elasticitymentioning

confidence: 74%

“…Indeed this instability was found in the homogenized response of the non-Hermitian elastic material obtained by Bordiga et al. [201] through the homogenization of a grid of elastic rods, figure 8 a . In this way, a formal link has been discovered between structural flutter and its occurrence in a continuum.…”

Section: Recent Progress On Fluttermentioning

confidence: 75%

“…A way to obtain a non-Hermitian elastic material has been indicated by Bordiga et al. [201] through the rigorous homogenization of a periodic grid of elastic rods (deformable under axial and shear forces and bending moment) subject to follower, periodically distributed, microforces , as shown in figure 8 a . The energy exchange with the surroundings is provided by the microforces.…”

Section: Recent Progress On Fluttermentioning

confidence: 99%

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Flutter instability in solids and structures, with a view on biomechanics and metamaterials

Bigoni,

Dal Corso,

Kirillov

et al. 2023

Proc. R. Soc. A.

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The phenomenon of oscillatory instability called ‘flutter’ was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving non-conservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps and new perspectives for investigations are indicated.

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Section: (D) Metamaterials and Non-hermitian Elasticitymentioning

confidence: 74%

Section: Recent Progress On Fluttermentioning

confidence: 75%

Section: Recent Progress On Fluttermentioning

confidence: 99%

See 1 more Smart Citation

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

Bigoni,

Dal Corso,

Kirillov

et al. 2023

Proc. R. Soc. A.

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“…Another misconception is that the lack of the major symmetry implies that the effective continuum does not have a strain potential and therefore can produce energy when deformed in closed loops in strain space [1]. This statement is correct to an infinitesimal strain cycle with linear elasticity, in which the Betti reciprocity and the superposition principles can be applied [5,1]. However, for lattice-based materials, even though the linear elastic bonds are assumed, the effective elastic behavior is nonlinear.…”

Section: Impacts To the Theory Of Elasticitymentioning

confidence: 99%

Anisotropy and Asymmetry of the Elastic Tensor of Lattice Materials

Yin

Liu

2023

J Elast

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Lattice materials formed by hinged springs or elastic bonds may exhibit diverse anisotropy and asymmetry features of the overall elastic behavior depending on their unit cell configuration. The recently developed singum model transfers the force-displacement relationship of the springs in the lattice to the stress-strain relationship in the continuum particle, and provides the analytical form of tangential elasticity. When a pre-stress exists in the lattice, the stiffness tensor significantly changes due to the effect of the configurational stress. Different lattice structures lead to different symmetry of the stiffness tensors, which is demonstrated by five lattices. When all bonds exhibit the same length, regular hexagonal, honeycomb, and auxetic lattices demonstrate that the stiffness changes from an isotropic to anisotropic, from symmetric to asymmetric tensor. When the central symmetry of the unit cell is not satisfied, the primitive cell will contain more than one singums and the Cauchy-Born rule fails by the loss of equilibrium of the single singum. A secondary stress is induced to balance the singums, which may lead to the loss of minor symmetry of the stiffness tensor. Displacement gradient d i j = u j,i is proposed to replace strain in the constitutive law for the general case because u 1,2 and u 2,1 may produce different stress states. Although the honeycomb lattice still exhibits isotropic behavior, for general auxetic lattices, an anisotropic and asymmetric elasticity is obtained with the loss of both minor and major symmetry, which is also demonstrated in a square lattice with unbalanced central symmetry and a chiral lattice. The modeling procedure and results may be generalized to three dimension and other lattices with the anisotropic and asymmetric stiffness.

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“…In elastodynamic reciprocity identifies the symmetry between action and reaction in solids and can be expressed as a convolution between two elastic states [10,11]. Reciprocity breaks down in the case of structured space-dependent and time-dependent constitutive properties [12,13], constitutive nonlinearity [14,15], external bias [16,17] and non-conservative follower forces [18].…”

Section: Introductionmentioning

confidence: 99%

Direction-selective non-reciprocal mechanical energy splitter

Rakhimzhanova

Brun

2022

Phil. Trans. R. Soc. A.

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A direction-selective elastic micro-structured medium is proposed. The lattice model combines constitutive nonlinearity, a threshold activation displacement and the gyroscopic effect of an isolated spinner to induce a tunable wave deviation on a selected direction in a full non-reciprocal way. The direction-selective effect is quantified in terms of energy flux dependence on gyricity and propagation velocity of the incident wave. Three different regimes are identified, addressed as passing, highly directive and barrier. The nonlinear system sustains solitary waves, described both numerically and through an analytical approximation, which show that the wave is univocally determined by the propagation velocity. A final analysis demonstrates the non-reciprocal mechanism originated by the proposed micro-structured medium. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)’.

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A way to hypo-elastic artificial materials without a strain potential and displaying flutter instability

Cited by 8 publications

References 33 publications

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

Anisotropy and Asymmetry of the Elastic Tensor of Lattice Materials

Direction-selective non-reciprocal mechanical energy splitter

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