Continuum micro-dilatation modeling of auxetic metamaterials

Lurie, S. A.; Kalamkarov, Alexander L.; Solyaev, Yury; Ustenko, Anastasia; Волков, А. А.

doi:10.1016/j.ijsolstr.2017.09.022

Cited by 24 publications

(5 citation statements)

References 45 publications

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“…This definition allows us to prove that the micro-dilatation theory is a special case of Mindlin’s linear elasticity with microstructure [8] obtained when the micro-deformation tensor is spherical [10, 46]. Established results state also that the micro-dilatation field can be treated as a scalar measure of the field of defects [12, 13, 47] and that it can be related with fluid pressure inside porous materials [45] or with micro-deformation of unit cells in auxetic lattices [35].…”

Section: Second Gradient Medium With Micro-dilatationmentioning

confidence: 99%

“…Recently, it has been shown that generalized continuum models, with updated non-standard numerical methods [29–31], allow for the description of a wide class of architectured mechanical metamaterials possessing a microstructure of, among others, composite, chiral, re-entrant, lattice type (see e.g. [32–36]). In [37–40] it has been shown that second gradient elasticity theory and its special cases can be efficiently used to predict mechanical behavior of pantographic metamaterials [38] made of long intersecting beams connected by hinges.…”

Section: Introductionmentioning

confidence: 99%

“…In [12, 13, 41] it has been shown that additional scalar field variables introduced in micro-dilatation elasticity can be treated as fields of defects. An increase in this function results in a decrease of the apparent elastic constants at a given point of the medium [10, 13, 35, 42]. Apparent elastic stiffness is also reduced when increasing strain/micro-dilatation coupling effects [41].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the dependence of standard and gradient elastic material constants on a field of defects

Solyaev¹,

Lurie

Barchiesi

et al. 2019

Mathematics and Mechanics of Solids

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In this work, we consider a strain gradient elasticity theory with an extended number of field variables: the displacement vector and an additional scalar field defining the internal micro-deformation. The total internal energy of the model depends on the strain, the micro-deformation function, their gradients, and the coupling. The considered model can be treated as gradient/micromorphic. Moreover, the micro-deformation field can be treated as a field of scalar defects distributed along the medium. Based on analytic (one-dimensional) solutions of uniform/non-uniform deformation of the rod, we introduce (i) an apparent stiffness and (ii) an apparent length scale parameter. Subsequently, we provide a variant of continuum-on-continuum homogenization by equating tip displacements for the gradient/micromorphic medium and an equivalent strain gradient one. Elongation of the gradient/micromorphic rod is therefore equated with the corresponding elongation of the equivalent strain gradient rod, whose behavior is characterized by the apparent material constants. Subsequently, the non-dimensional coupling number is identified with a damage parameter. It is shown that, on the one hand, the apparent stiffness of the rod is reduced when such parameter increases. On the other hand, the apparent length scale parameter (i.e. the apparent second gradient elastic coefficient) increases when the damage parameter increases. Therefore, it is shown that the presence of defects in a second gradient linear elastic material may increase its apparent strain gradient behavior.

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Section: Second Gradient Medium With Micro-dilatationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the dependence of standard and gradient elastic material constants on a field of defects

Solyaev¹,

Lurie

Barchiesi

et al. 2019

Mathematics and Mechanics of Solids

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“…Yuri Solyaev, in his presentation (''Continuum micro-dilatation modeling of auxetic metamaterials with re-entrant lattice structure''), discussed the modelling of metamaterials with re-entrant type lattice structure. The micro-dilatation theory [57], which takes into account the coupling between deformations of porous media and volume fraction of voids that changes in the process of deformation, has been described and its effectiveness was proven in describing the mechanical behaviour of cellular metamaterials with negative Poisson's ratio.…”

Section: Architectured and Meta-materialsmentioning

confidence: 99%

Workshop on Encounter of the third kind on Generalized continua and microstructures in Arpino, 3–7 April 2018: A review of presentations and discussions

Laudato

Angelo

2019

Mathematics and Mechanics of Solids

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The present article is a rational report of the workshop Encounter of the third kind on Generalized continua and microstructures (Arpino, 3–7 April 2018). The main goal of the workshop was to gather together experts in the framework of generalized continuum theories and microstructured materials to discuss and analyse the recent advancements in the field. The interested reader will find in this article a general discussion of the motivations and of the main topics discussed during the workshop as well as a detailed report of the talks and the relative bibliography. All the talks have been recorded and it is possible to watch them on the M&MOCS YouTube channel at https://www.youtube.com/playlist?list=PLWzlK5oO41smkt5HtiDQJV7nsbz5wnD01

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“…detailed kinematic fields and higher order gradient terms in their equations of motion to capture their unusual behavior. Examples are represented by pantographic structures [3][4][5][6][7], for which their exotic behavior has to be described with higher gradient continuum theories [8][9][10] or micromorphic theories [11,12], granular media [13][14][15][16][17][18][19], auxetic material [20,21] and functionally graded material [22,23].…”

Section: Introductionmentioning

confidence: 99%

Parametric Experimentation on Pantographic Unit Cells Reveals Local Extremum Configuration

et al. 2019

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Pantographic metamaterials are known for their ability to have large deformation while remaining in the elastic regime. We have performed a set of experiments on 3D printed pantographic unit cells to parametrically investigate their response when undergoing tensile, compression, and shear loading with the aim of i) studying the role of each parameter in the resultant mechanical behavior of the sample, and ii) providing a benchmark for the mathematical models developed to describe pantographic structures. Results show the existence of local extrema in the space of the geometrical parameters, suggesting the use of optimization techniques to find optimal geometrical parameters resulting in desired functionalities. We have also performed tensile relaxation tests on the samples, with the results indicating the complexity of the dynamic behavior and the existence of multiple relaxation characteristic times. Such results can be used to for calibrating mathematical models describing pantographic structures under dynamic loadings.

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Continuum micro-dilatation modeling of auxetic metamaterials

Cited by 24 publications

References 45 publications

On the dependence of standard and gradient elastic material constants on a field of defects

On the dependence of standard and gradient elastic material constants on a field of defects

Workshop on Encounter of the third kind on Generalized continua and microstructures in Arpino, 3–7 April 2018: A review of presentations and discussions

Parametric Experimentation on Pantographic Unit Cells Reveals Local Extremum Configuration

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