Derivation of imperfect interface models coupling damage and temperature

Bonetti, Elena; Bonfanti, Giovanna; Lebon, Frédéric

doi:10.1016/j.camwa.2018.09.027

Cited by 7 publications

(6 citation statements)

References 25 publications

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“…We will denote by DW λ,µ (e) its differential at any e ∈ R 3×3 sym . Observe that 2W λ,µ (e) = DW λµ (e) • e ≥ 2µ|e| 2 for all e ∈ R 3×3 sym .…”

Section: Setup Of the Problemmentioning

confidence: 99%

“…One possibility is to develop a formal asymptotic expansion method as in [14,7,12]. For damage and delamination, we refer to the asymptotic analyses carried out in [1,2]. In the context of rateindependent modeling of delamination, instead, Γ-convergence type techniques were used in [19] to show that Energetic solutions to a system for isotropic damage converge to an Energetic solution of a delamination model as the thickness of the layer between the two bulk bodies, where damage occurs, tends to zero.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of two linearly elastic bodies connected by a heavy thin soft viscoelastic layer

Bonetti¹,

Bonfanti²,

Licht³

et al. 2019

Preprint

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In this paper we extend the asymptotic analysis in [18], performed on a structure consisting of two linearly elastic bodies connected by a thin soft nonlinear KelvinVoigt viscoelastic adhesive layer, to the case in which the total mass of the layer remains strictly positive as its thickness tends to zero.We obtain convergence results by means of a nonlinear version of Trotter's theory of approximation of semigroups acting on variable Hilbert spaces. Differently from the limit models derived in [18], in the present analysis the dynamic effects on the surface on which the layer shrinks do not disappear. Thus, the limiting behavior of the remaining bodies is described not only in terms of their displacements on the contact surface, but also by an additional variable that keeps track of the dynamics in the adhesive layer.

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“…We will denote by DW λ,µ (e) its differential at any e ∈ R 3×3 sym . Observe that 2W λ,µ (e) = DW λµ (e) • e ≥ 2µ|e| 2 for all e ∈ R 3×3 sym .…”

Section: Setup Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of two linearly elastic bodies connected by a heavy thin soft viscoelastic layer

Bonetti¹,

Bonfanti²,

Licht³

et al. 2019

Preprint

Self Cite

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show abstract

“…It turned out that the damage theory can be successfully used for describing adhesive contact between solids. In [25], they introduced a model describing a layered structure composed by adhesive subject to a degradation process. By an asymptotic expansion method, they derived a model of imperfect interface coupling damage and temperature evolution.…”

Section: Introductionmentioning

confidence: 99%

Study on Establishing Degradation Model of Chip Solder Joint Material under Coupled Stress

Jing

2020

Materials

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The chip is the core component of the integrated circuit. Degradation and failure of chip solder joints can directly lead to function loss of the integrated circuit. In order to establish the degradation model of chip solder joints under coupled stress, this paper takes quad flat package (QFP) chip solder joints as the study object. First, solder joint degradation data and failure samples were obtained through fatigue tests under coupled stress. Three types of micro failure modes of solder joints were obtained by scanning electron microscope (SEM) analysis and finite element model (FEM) simulation results. Second, the characterization of degradation data was obtained by the principal component of Mahalanobis distance (PCMD) algorithm. It is found that solder joint degradation is divided into three stages: strain accumulation stage, crack propagation stage, and failure stage. Later, Coffin–Manson model and Paris model were modified based on the PCMD health index and strain simulation. The function relationship between strain accumulation time, crack propagation time, and strain was determined, respectively. Solder joint degradation models at different degradation stage were established. Finally, through strain simulation, the models can predict the strain accumulation time and failure time effectively under each failure mode, and their prediction accuracy is above 85%.

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“…After that, intensive studies have been carried out on this type of equations, see, e.g., [15,16,17] for more details. Moreover, this type of equations appear in various applications: irreversible phase change modeling [21], reaction-diffusion with absorption problems in Biochemistry [21], irreversible damage and fracture evolution analysis [10,11,19] and recently in constrained stratigraphic problems in Geology [1,2,3,4,24]. Concerning the study of Barenblatt equations with a stochastic force term, a few papers have been written.…”

Section: Introductionmentioning

confidence: 99%

“…Goal of the study. In the study of composite or bonded structures, temperature effects in the evolution of damage at the interface can not be ignored, it is even a fundamental coupling [11,25]. Additionally, the introduction of stochastic and random effects is also important from a modeling point of view in order to take into account several phenomena such as microscopic fluctuations, random forcing effects of interscale interactions.…”

Section: Introductionmentioning

confidence: 99%

Well-posedness for the coupling of a random heat equation with a multiplicative stochastic Barenblatt equation

Bauzet¹,

Lebon²,

Maitlo³

et al. 2019

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In this contribution, a stochastic nonlinear evolution system under Neumann boundary conditions is investigated. Precisely, we are interested in finding an existence and uniqueness result for a random heat equation coupled with a Barenblatt's type equation with a multiplicative stochastic force in the sense of Itô. In a first step we establish well-posedness in the case of an additive noise through a semi-implicit time discretization of the system. In a second step, the derivation of continuous dependence estimates of the solution with respect to the data allows us to show the desired existence and uniqueness result for the multiplicative case. * For a given separable Hilbert space X, we denote by N 2 w (0, T, X) the space of predictable Xvalued processes endowed with the norm ||φ|| 2 N 2 w (0,T,X) = E T 0 ||φ|| 2 X dt (see Da Prato-Zabczyk [14] p.94).

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Derivation of imperfect interface models coupling damage and temperature

Cited by 7 publications

References 25 publications

Dynamics of two linearly elastic bodies connected by a heavy thin soft viscoelastic layer

Dynamics of two linearly elastic bodies connected by a heavy thin soft viscoelastic layer

Study on Establishing Degradation Model of Chip Solder Joint Material under Coupled Stress

Well-posedness for the coupling of a random heat equation with a multiplicative stochastic Barenblatt equation

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