Viscoelastic truss metamaterials as time-dependent generalized continua

Glaesener, Raphaël N.; Bastek, Jan-Hendrik; Gonon, Frederick; Kannan, Vignesh; Telgen, Bastian; Spöttling, Ben; Steiner, Stephan; Kochmann, Dennis M.

doi:10.1016/j.jmps.2021.104569

Cited by 22 publications

(7 citation statements)

References 41 publications

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“…Statically, a conformal mapping approach has showed excellent quantitative agreement in modelling mechanism based metamaterials [65]. More-over, Glaesener et al have even shown that viscoelastic truss-based metamaterials can be modelled as time-dependent continua [66]. In doing so, they managed to capture the full nonlinear dynamics of the metamaterials accurately.…”

Section: Modelling Viscoelastic Metamaterialsmentioning

confidence: 99%

The Extreme Mechanics of Viscoelastic Metamaterials

Dykstra¹,

Janbaz²,

Coulais³

2022

Preprint

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Mechanical metamaterials made of flexible building blocks can exhibit a plethora of extreme mechanical responses, such as negative elastic constants, shape-changes, programmability and memory. To date, dissipation has largely remained overlooked for such flexible metamaterials. As a matter of fact, extensive care has often been devoted in the constitutive materials' choice to avoid strong dissipative effects. However, in an increasing number of scenarios, where metamaterials are loaded dynamically, dissipation can not be ignored. In this review, we show that the interplay between mechanical instabilities and viscoelasticity can be crucial and can be harnessed to obtain new functionalities. We first show that this interplay is key to understanding the dynamical behaviour of flexible dissipative metamaterials that use buckling and snapping as functional mechanisms. We further discuss the new opportunities that spatial patterning of viscoelastic properties offer for the design of mechanical metamaterials with properties that depend on loading rate.

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Section: Modelling Viscoelastic Metamaterialsmentioning

confidence: 99%

The Extreme Mechanics of Viscoelastic Metamaterials

Dykstra¹,

Janbaz²,

Coulais³

2022

Preprint

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“…Based on these effective models, many metamaterials with excellent acoustic characteristics have been designed and studied [48][49][50][51] . Moreover, both Maxwell and Kelvin-Voigt materials show additional resistance to fast deformations [15][16][17] , providing models that can be extended to metamaterials [18][19][20][21][22] . For instance, based on the Kelvin-Voigt model, Janbaz et al used bi-beams composed of a hyperelastic beam and a visco-hyperelastic beam in parallel as the elements to design mechanical metamaterials with varying deformation characteristics and strain rate-dependent mechanical response 52 .…”

Section: Introductionmentioning

confidence: 99%

“…Metamaterials with tunable mechanical properties [11][12][13][14] , in particular having a rich dynamical behavior [15][16][17][18][19][20][21][22] or exhibiting non-reciprocity 23,24 , are extremely attractive for numerous applications, such as control of the propagation of acoustic and elastic waves [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] . Beyond the homogenization limit, the idea of dynamic shear, bulk, or mass density is commonly used and accepted for waves 41 .…”

Section: Introductionmentioning

confidence: 99%

Non-reciprocal and Non-Newtonian Mechanical Metamaterials

Wang

Martínez

Ulliac

et al. 2023

Preprint

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Non-Newtonian liquids are characterized by a stress and velocity-dependent dynamical response. In elasticity, and in particular in the field of phononics, reciprocity in the equations acts against obtaining a directional response for passive media. Active stimuli-responsive materials have been conceived to overcome it. Significantly, Milton and Willis have shown theoretically in 2007 that quasi-rigid bodies containing masses at resonance can display a very rich dynamical behavior, hence opening a route toward the design of non-reciprocal and non-Newtonian metamaterials. In this paper, we design a solid structure that displays unidirectional shock resistance, thus going beyond Newton’s second law in analogy to non-Newtonian fluids. We design the mechanical metamaterial with finite element analysis and fabricate it using 3D printing at the centimetric scale (with fused deposition modeling – FDM) and at the micrometric scale (with two-photon lithography – TPL). The non-Newtonian elastic response is measured via dynamical velocity-dependent experiments. Reversing the direction of the impact, we further highlight the intrinsic non-reciprocal response.

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“…Generalized mechanics has been widely investigated in the literature. It has been implemented for problems of elasticity [9][10][11][12][13]; plasticity [14][15][16][17][18][19]; damage modeling [20][21][22][23][24][25]; modeling metamaterials [26][27][28] such as pantographic structures [29][30][31], network materials [32], viscoelastic truss structures [33], bipantographic structures [34], second gradient fluids [35]; gradient-enhanced homogenization [36][37][38][39]; micropolar continua [40]; fracture mechanics [41]; biomechanics [42][43][44]; and anisotropic systems [45]. Parameter determination of generalized mechanics models has been studied for static and dynamic regimes in Shekarchizadeh et al [46,47], respectively.…”

Section: Introductionmentioning

confidence: 99%

A benchmark strain gradient elasticity solution in two-dimensions for verifying computational approaches by means of the finite element method

Shekarchizadeh

Abali

Bersani

2022

Mathematics and Mechanics of Solids

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In elasticity, microstructure-related deviations may be modeled by strain gradient elasticity. For so-called metamaterials, different implementations are possible for solving strain gradient elasticity problems numerically. Analytical solutions of simple problems are used to verify the numerical approach. We demonstrate such a case in a two-dimensional continuum as a benchmark case for computations. As strain gradient enforces higher regularity conditions in displacements, in the finite element method (FEM), the use of standard elements is often seen as inadequate. For such piecewise or elementwise continuous elements, we examine a possible remedy to correctly simulate strain gradient elasticity problems by implementing two techniques. First, we enforce continuity of displacement gradient across elements; second, we employ a mixed finite element method where displacement and its gradient are solved both as unknowns. The results show the pros and cons of each numerical technique. All methods converge monotonically, but the mixed method is more reliable than the other one.

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Viscoelastic truss metamaterials as time-dependent generalized continua

Cited by 22 publications

References 41 publications

The Extreme Mechanics of Viscoelastic Metamaterials

The Extreme Mechanics of Viscoelastic Metamaterials

Non-reciprocal and Non-Newtonian Mechanical Metamaterials

A benchmark strain gradient elasticity solution in two-dimensions for verifying computational approaches by means of the finite element method

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