A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media

Benveniste, Y.

doi:10.1016/j.jmps.2005.10.009

Cited by 271 publications

(269 citation statements)

References 47 publications

(72 reference statements)

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“…Because r is the distance to the mid-surface, the ( ) , , p q r coordinate system is parallel curvilinear as defined by Benveniste [32].…”

Section: Discussionmentioning

confidence: 99%

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On the Alternate Direction Implicit (ADI) Method for Solving Heat Transfer in Composite Stamping

Lévy¹,

Hoang²,

Corre³

2017

MSA

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Thermostamping of thermoplastic matrix composites is a process where a preheated blank is rapidly shaped in a cold matching mould. Predictive modelling of the main physical phenomena occurring in this process requires an accurate prediction of the temperature field. In this paper, a numerical method is proposed to simulate this heat transfer. The initial three-dimensional heat equation is handled using an additive decomposition, a thin shell assumption, and an operator splitting strategy. An adapted resolution algorithm is then presented. It results in an alternate direction implicit decomposition: the problem is solved successively as a 2D surface problem and several onedimensional through thickness problems. The strategy was fully validated versus a 3D calculation on a simple test case and the proposed strategy is shown to enable a tremendous calculation speed up. The limits of applicability of this method are investigated with two parametric studies, one on the thickness to width ratio and the other one on the effect of curvature. These conditions are usually fulfilled in industrial cases. Finally, even though the method was developed under linear assumption (constant material properties), the strategy validity is extended to multiply, temperature dependant (nonlinear) case using an industrial test case. Because of the standard methods involved, the proposed ADI method can readily be implemented in existing software.

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“…Because r is the distance to the mid-surface, the ( ) , , p q r coordinate system is parallel curvilinear as defined by Benveniste [32].…”

Section: Discussionmentioning

confidence: 99%

“…This definition follows the framework adopted by Benveniste [32] in the case of a thin interphase. A similar approach is fully detailed in three dimensions by Bognet et al [33] in their appendix.…”

Section: Appendix Arbitrary Curvilinear Shell Descriptionmentioning

confidence: 99%

On the Alternate Direction Implicit (ADI) Method for Solving Heat Transfer in Composite Stamping

Lévy¹,

Hoang²,

Corre³

2017

MSA

View full text Add to dashboard Cite

show abstract

“…This kind of simplification of the interface is not enough to reflect various damage occurring on the interface (e.g., debonding, sliding and/or cracking across the interface), and as a result the concept of imperfect interface should be incorporated. Up to now various imperfect interface models have been proposed in the context of heat conduction [10][11][12], dielectricity [13,14] and elasticity [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…The imperfect interface studied here is mechanically compliant and thermally (or dielectrically) weakly (or highly) conducting. For a mechanically compliant interface, we adopt the linear spring model for the imperfect interface [15][16][17][18][19]. In this model, tractions are continuous but displacements are discontinuous across the imperfect interface, jumps in the displacement components are further assumed to be proportional, in terms of the 'spring-factor-type' interface parameters, to their respective interface traction *Address correspondence to this author at the Dept.…”

Section: Introductionmentioning

confidence: 99%

“…For a thermally (or dielectrically) weakly conducting interface [10][11][12][13], the normal heat flux (or the normal electric displacement) is continuous but the temperature (or electric potential) is discontinuous across the interface, the jump in temperature (or electric potential) is proportional to the normal heat flux (or normal electric displacement). For a thermally (or dielectrically) highly conducting interface [11,12,18], the temperature (or electric potential) is continuous across the interface whereas the normal heat flux (or normal electric displacement) has a discontinuity across the interface, which is proportional to a certain differential expression of the temperature (or electric potential). It is not a easy task to address this problem since the interface is imperfect in heat conduction, elasticity and dielectricity.…”

Section: Introductionmentioning

confidence: 99%

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Exact Solutions for Simply Supported and Multilayered Piezothermoelastic Plates with Imperfect Interfaces

Wang¹,

Pan²

2007

TOMECHJ

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Exact solutions are derived for three-dimensional, orthotropic, linearly piezothermoelastic, simply-supported, and multilayered rectangular plates with imperfect interfaces under static thermo-electro-mechanical loadings. In this research the imperfect interface is described as thermally weakly (or highly) conducting, mechanically compliant and dielectrically weakly (or highly) conducting. While the homogeneous solutions for one layer are obtained in terms of the socalled pseudo-Stroh formalism, solutions for multilayered plates are expressed in terms of the transfer matrices for both the layer and the imperfect interface. Due to the fact that the thermal effect is incorporated, we adopt a special form of the transfer matrix, resulting in a very concise solution structure for piezothermoelastic multilayered plates. Numerical results are presented to validate the developed formulas and to demonstrate the influence of the interface imperfection on the distributions of the field variables.

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A General Piezoelectric Interface Model: Coordinate‐free Asymptotic Derivation and Application to the Homogenization of Piezoelectric Composites

Gu¹,

He²,

Pensée³

2007

Particle and Continuum Aspects of Mesomechanics

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A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media

Cited by 271 publications

References 47 publications

On the Alternate Direction Implicit (ADI) Method for Solving Heat Transfer in Composite Stamping

On the Alternate Direction Implicit (ADI) Method for Solving Heat Transfer in Composite Stamping

Exact Solutions for Simply Supported and Multilayered Piezothermoelastic Plates with Imperfect Interfaces

A General Piezoelectric Interface Model: Coordinate‐free Asymptotic Derivation and Application to the Homogenization of Piezoelectric Composites

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