Dynamics of elastic bodies connected by a thin adhesive layer

Licht, Christian; Lebon, Frédéric; Léger, Alain

doi:10.1007/978-3-540-89105-5_9

Cited by 8 publications

(8 citation statements)

References 6 publications

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“…Adhesively bonded joints are an attractive way to put together the components of a structure. As in several situations thermal effects are not negligible, we extend a previous study [1] devoted to a linearly elastic material to the linearly thermoelastic case. Taking advantage of the coupling between mechanical and thermal effects, it is still possible to formulate the problem of determining the transient response of a structure made of two linearly thermoelastic bodies perfectly connected by a thin soft thermoelastic layer with high thermal resistivity in terms of an evolution equation in a Hilbert space of possible states (displacement, temperature, velocity) with finite energy.…”

Section: Introductionmentioning

confidence: 76%

“…Taking advantage of the coupling between mechanical and thermal effects, it is still possible to formulate the problem of determining the transient response of a structure made of two linearly thermoelastic bodies perfectly connected by a thin soft thermoelastic layer with high thermal resistivity in terms of an evolution equation in a Hilbert space of possible states (displacement, temperature, velocity) with finite energy. Hence it is possible to adopt the strategy of [1,2] in order to, first, obtain existence and uniqueness results and, then, to study the asymptotic behavior when some geometrical and thermomechanical data, now regarded as parameters, tend to their natural limits. The limit behavior which supports our proposal of a simplified but accurate enough model for the initial physical situation, corresponds to the dynamic response to the initial load of two linearly thermoelastic bodies connected by a thermomechanical constraint along the surface the adhesive layer shrinks to.…”

Section: Introductionmentioning

confidence: 99%

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Transient response of thermoelastic bodies linked by a thin layer of low stiffness and high thermal resistivity

Licht¹,

Khaoua²,

Weller³

2014

Comptes Rendus. Mécanique

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Section: Introductionmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Transient response of thermoelastic bodies linked by a thin layer of low stiffness and high thermal resistivity

Licht¹,

Khaoua²,

Weller³

2014

Comptes Rendus. Mécanique

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“…Stiffness and mass values are expected to be connected, although not necessarily in a trivial way, to the contact quality [ 19 , 20 ]. More recently, rational derivations based on asymptotic expansion have been proposed, yielding similar spring-mass models of imperfect interface [ 21 ]. These imperfect conditions arise from a homogenization process of a thin interphase.…”

Section: Introductionmentioning

confidence: 99%

High-frequency homogenization in periodic media with imperfect interfaces

et al. 2020

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In this work, the concept of high-frequency homogenization is extended to the case of one-dimensional periodic media with imperfect interfaces of the spring-mass type. In other words, when considering the propagation of elastic waves in such media, displacement and stress discontinuities are allowed across the borders of the periodic cell. As is customary in high-frequency homogenization, the homogenization is carried out about the periodic and antiperiodic solutions corresponding to the edges of the Brillouin zone. Asymptotic approximations are provided for both the higher branches of the dispersion diagram (second-order) and the resulting wave field (leading-order). The special case of two branches of the dispersion diagram intersecting with a non-zero slope at an edge of the Brillouin zone (occurrence of a so-called Dirac point) is also considered in detail, resulting in an approximation of the dispersion diagram (first-order) and the wave field (zeroth-order) near these points. Finally, a uniform approximation valid for both Dirac and non-Dirac points is provided. Numerical comparisons are made with the exact solutions obtained by the Bloch–Floquet approach for the particular examples of monolayered and bilayered materials. In these two cases, convergence measurements are carried out to validate the approach, and we show that the uniform approximation remains a very good approximation even far from the edges of the Brillouin zone.

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“…On the one hand, in the linear case, imperfect interface models amounts to typical "spring-mass" transmissions conditions, see [41,6,4,38]. Note that some of these phenomenological models can also be seen as effective models for thin interphase bonds between solids, which has been demonstrated by asymptotic analysis [28,26]. On the other hand, the use of non-linear transmission conditions can be necessary to model more complex interface phenomena, such as the generation of higher-or sub-harmonics, DC response, hysteretic or chaotic behaviors, slow dynamics, see e.g.…”

mentioning

confidence: 99%

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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Dynamics of elastic bodies connected by a thin adhesive layer

Cited by 8 publications

References 6 publications

Transient response of thermoelastic bodies linked by a thin layer of low stiffness and high thermal resistivity

Transient response of thermoelastic bodies linked by a thin layer of low stiffness and high thermal resistivity

High-frequency homogenization in periodic media with imperfect interfaces

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

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