Numerical modeling of a composite auxetic metamaterials using micro-dilatation theory

Solyaev, Yury; Lurie, S. A.; Ustenko, Anastasia

doi:10.1007/s00161-018-0730-y

Cited by 17 publications

(7 citation statements)

References 31 publications

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“…It seems that the same results may be proven in the two-dimensional and three-dimensional problems by using generalized analytical and numerical approaches of strain gradient and micro-dilatation elasticity theories [36,41,58,59]. However, it might be necessary to consider more general models to describe the field of defects in materials with complex microstructure, such as micropolar, microstretch, or general micromorphic [9].…”

Section: Discussionmentioning

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%

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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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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: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…В [25] методом Петрова -Галеркина исследовано влияние пористости на напряжения (а meshless local Petrov -Galerkin). Численное трехмерное моделирование композитных ячеистых метаматериалов представлено в [26].…”

Section: Introductionunclassified

Relative Pore Volume Under Indentation of Porous Materials

Zelentsov

Zagrebneva

Lapina

et al. 2021

PSP

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Investigation of the function of the relative volume of pores under the load action is carried out on the base of the solution of the static contact problem of the indentation of a layer made of a material with voids or unfilled pores. A rigid strip indenter with a flat base is pressed into a porous layer that is adhered to a non-deformable base along the lower boundary. The formulated 3D problem of the indentation of a porous layer is reduced to solving the plane contact problem of the indentation of a porous strip. The plane contact problem is reduced to solving an integral equation for unknown contact stresses, the solution of which is constructed by the method of successive approximations in the form of an asymptotic expansion in the dimensionless parameter of the problem. The obtained contact stresses and the force acting on the indenter made it possible to study the influence of the nonclassical moduli of the layer porous material (the connectivity modulus and pore rigidity modulus) on the main contact characteristics and on the distribution of the function of the relative pore volume. The connectivity modulus increase leads to an increase in the compliance of the layer porous material, the pore rigidity modulus increase leads to an increase in the rigidity of the layer porous material. The maximum value of the distribution function of the relative pore volume in the porous material of the layer is achieved under the indenter base centre, regardless of the change in the porous material non-classical moduli.

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“…Porous materials are frequently modeled as a full material with voids as given inclusions at the microscale, we refer to [28][29][30][31][32][33]. Additive manufacturing is capable of building metamaterials as demonstrated in [34][35][36][37][38][39]. Also adding texture in 3-D printing introduces a substructure.…”

Section: Introductionmentioning

confidence: 99%

Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization

Abali

Barchiesi

2020

Continuum Mech. Thermodyn.

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Metamaterials exhibit materials response deviation from conventional elasticity. This phenomenon is captured by the generalized elasticity as a result of extending the theory at the expense of introducing additional parameters. These parameters are linked to internal length scales. Describing on a macroscopic level, a material possessing a substructure at a microscopic length scale calls for introducing additional constitutive parameters. Therefore, in principle, an asymptotic homogenization is feasible to determine these parameters given an accurate knowledge on the substructure. Especially in additive manufacturing, known under the infill ratio, topology optimization introduces a substructure leading to higher-order terms in mechanical response. Hence, weight reduction creates a metamaterial with an accurately known substructure. Herein, we develop a computational scheme using both scales for numerically identifying metamaterials parameters. As a specific example, we apply it on a honeycomb substructure and discuss the infill ratio. Such a computational approach is applicable to a wide class substructures and makes use of open-source codes; we make it publicly available for a transparent scientific exchange.

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Numerical modeling of a composite auxetic metamaterials using micro-dilatation theory

Cited by 17 publications

References 31 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

Relative Pore Volume Under Indentation of Porous Materials

Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization

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