Effective Properties of Non-Linear Elastic Laminated Composites with Perfect and Imperfect Contact Conditions

López-Realpozo, J.C.; Rodrı́guez-Ramos, Reinaldo; Guinovart-Dı́az, Raúl; Bravo‐Castillero, Julián; Pérez-Fernández, Leslie D.; Sabina, Federico J.; Maugin, Gérard A.

doi:10.1080/15376490801977742

Cited by 10 publications

(16 citation statements)

References 35 publications

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“…We want to define the material properties of the homogeneous specimen in such a way that both specimens demonstrate the same overall responses (the same overall stresses) when subjected to the same overall deformations. This definition of equivalency of laminated material and homogeneous material is in accordance with the homogenization [e.g., 8,9] and multiscate [e.g., 10,11] theories and finite element approach [e.g., 12,13], as well as an approach based on the ideas of mechanics of inhomogeneous solids [e.g., 14,15].…”

Section: Homogenized Constitutive Equations For Laminated Compositementioning

confidence: 98%

Overall and Local Effects in Laminated Elastic Composite Under Nonlinear Strains

Kolpakov

Rakin

2010

Mechanics of Advanced Materials and Structures

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It is known [1-4] that composite materials can possess properties different from the properties of their constitutive elements.There are few examples demonstrating significant (not quantitatively, but qualitatively too) change of properties. This article presents new effects of such kind. It is shown that laminated composite material made of linear elastic layers demonstrates nonlinear "overall" material properties when subjected to nonlinear deformations. This effect can be described as "the transformation of geometrical nonlinearity in material nonlinearity" in a laminated composite. Also, it is found that the local stresses in layers can be disproportionate to the elastic constants of layers under nonlinear deformations in opposition to the linear case.

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Section: Homogenized Constitutive Equations For Laminated Compositementioning

confidence: 98%

Overall and Local Effects in Laminated Elastic Composite Under Nonlinear Strains

Kolpakov

Rakin

2010

Mechanics of Advanced Materials and Structures

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“…where E 0 = ∂U 0 /∂X. The latter macroscopic strain field is therefore related to the macroscopic stress field Σ 0 by the effective constitutive relation (32), which we formally write as Σ 0 = G eff (E 0 ).…”

Section: Final Homogenized Modelmentioning

confidence: 99%

“…Remark 5. The zeroth-order stress-strain relation Σ 0 = G eff (E 0 ), in (32) or (33), is local in space and time and, as such, applies to the static case as well (its derivation in (18)(19)(20)(21)(22)(23)(24) only involves equations that are time-independent). In such a static configuration, it could also be directly obtained from (1)(2) as an exact relation between a macroscopic stress and an equivalent applied macroscopic strain associated with the prescribed body-force F .…”

Section: Remarkmentioning

confidence: 99%

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Effective dynamics for low-amplitude transient elastic waves in a 1D periodic array of non-linear interfaces

Bellis

Lombard

Touboul

et al. 2021

Journal of the Mechanics and Physics of Solids

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This article focuses on the time-domain propagation of elastic waves through a 1D periodic medium that contains non-linear imperfect interfaces, i.e. interfaces exhibiting a discontinuity in displacement and stress governed by a non-linear constitutive relation. The array considered is generated by a, possibly heterogeneous, cell repeated periodically and bonded by interfaces that are associated with transmission conditions of non-linear "spring-mass" type. More precisely, the imperfect interfaces are characterized by a linear dynamics but a non-linear elasticity law. The latter is not specified at first and only key theoretical assumptions are required. In this context, we investigate transient waves with both low-amplitude and long-wavelength, and aim at deriving homogenized models that describe their effective motion. To do so, the two-scale asymptotic homogenization method is deployed, up to the first-order. To begin, an effective model is obtained for the leading zeroth-order contribution to the microstructured wavefield. It amounts to a wave equation with a non-linear constitutive stress-strain relation that is inherited from the behavior of the imperfect interfaces at the microscale. The next first-order corrector term is then shown to be expressed in terms of a cell function and the solution of a linear elastic wave equation. Without further hypothesis, the constitutive relation and the source term of the latter depend non-linearly on the zeroth-order field, as does the cell function. Combining these zeroth-and first-order models leads to an approximation of both the macroscopic behavior of the microstructured wavefield and its small-scale fluctuations within the periodic array. Finally, particularizing for a prototypical non-linear interface law and in the cases of a homogeneous periodic cell and a bilaminated one, the behavior of the obtained models are then illustrated on a set of numerical examples and compared with full-field simulations. Both the influence of the dominant wavelength and of the wavefield amplitude are investigated numerically, as well as the characteristic features related to non-linear phenomena.

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“…In the present paper, a semi-analytical method is applied in order to solve the 2D non-linear homogenization problem of biaxial loading of multilayers. For two different points of view on homogenization of non-linear laminated composites we refer to Omri et al, 2000, Lopez-Realpozo et al, 2008, Zhu et al, 2018. For the analysis of effective behavior of elastic structures with non-linear periodicity we refer to Guinovart-Sanjuan et al, 2018 andDong et al, 2018.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

A model of heterogeneous thermoviscoplastic material preserving uniform normal strains under combined compression, tension (or compression) and shearing. Instability and homogenization results

Chatzigeorgiou

Charalambakis

2019

Composites Part B: Engineering

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Effective Properties of Non-Linear Elastic Laminated Composites with Perfect and Imperfect Contact Conditions

Cited by 10 publications

References 35 publications

Overall and Local Effects in Laminated Elastic Composite Under Nonlinear Strains

Overall and Local Effects in Laminated Elastic Composite Under Nonlinear Strains

Effective dynamics for low-amplitude transient elastic waves in a 1D periodic array of non-linear interfaces

A model of heterogeneous thermoviscoplastic material preserving uniform normal strains under combined compression, tension (or compression) and shearing. Instability and homogenization results

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