Investigation of the convergence of the mixed displacement-pressure formulation for three-dimensional poroelastic materials using hierarchical elements

Rigobert, Stéphane; Atalla, Noureddine; Sgard, Franck

doi:10.1121/1.1616579

Cited by 39 publications

(30 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…During the past decade, numerical methods such as finite element methods based on the Biot theory 1,2 have been widely developed for automotive and aeronautic industries. Classical methods consider the displacements of the solid and fluid phases as variables, 3,4 respectively u s and u f , or a mixed formulation 5,6 based on the displacement of the solid phase and the interstitial fluid pressure p. These numerical methods allow one to predict the structural and fluid couplings induced by the poroelastic medium without any kinematic or geometrical assumptions. However, for large size finite element models, these methods can require significant computational time.…”

Section: Introductionmentioning

confidence: 99%

Validity of the limp model for porous materials: A criterion based on the Biot theory

Doutres

Lanfranchi

Génevaux

et al. 2007

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

The validity of using the limp model for porous materials is addressed in this paper. The limp model is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. Being an equivalent fluid model accounting for the motion of the frame, it has fewer limitations than the usual equivalent fluid model assuming a rigid frame. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the frame stiffness influence ͑FSI͒, based on porous material properties. The critical values of FSI under which the limp model can be used are determined using a one-dimensional analytical modeling for two boundary sets: absorption of a porous layer backed by a rigid wall and radiation of a vibrating plate covered by a porous layer. Compared with other criteria, the criterion associated with FSI provides information in a wider frequency range and can be used for configurations that include vibrating plates.

show abstract

Section: Introductionmentioning

confidence: 99%

Validity of the limp model for porous materials: A criterion based on the Biot theory

Doutres

Lanfranchi

Génevaux

et al. 2007

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

show abstract

“…In addition to resulting in excessive calculation times, the convergence of the model is difficult to assure. This is a particular difficulty in the numerical solution of 3D models including porous materials, as the convergence criteria for these models are different from the classical criteria used in finite element modelling [7,9].…”

Section: Numerical Models Of Poroelastic Materialsmentioning

confidence: 99%

On the influence of frequency-dependent elastic properties in vibro-acoustic modelling of porous materials under structural excitation

Kelen

Göransson

Pluymers

et al. 2014

Journal of Sound and Vibration

View full text Add to dashboard Cite

a b s t r a c tThe aspects related to modelling the frequency dependence of the elastic properties of airsaturated porous materials have been largely neglected in the past for several reasons. For acoustic excitation of porous materials, the material behaviour can be quite well represented by models where the properties of the solid frame have little influence. Only recently has the importance of the dynamic moduli of the frame come into focus. This is related to a growing interest in the material behaviour due to structural excitation. Two aspects stand out in connection with the elastic-dynamic behaviour. The first is related to methods for the characterisation of the dynamic moduli of porous materials. The second is a perceived lack of numerical methods able to model the complex material behaviour under structural excitation, in particular at higher frequencies. In the current paper, experimental data from a panel under structural excitation, coated with a porous material, are presented. In an attempt to correlate the experimental data to numerical predictions, it is found that the measured quasi-static material parameters do not suffice for an accurate prediction of the measured results. The elastic material parameters are then estimated by correlating the numerical prediction to the experimental data, following the physical behaviour predicted by the augmented Hooke's law. The change in material behaviour due to the frequency-dependent properties is illustrated in terms of the propagation of the slow wave and the shear wave in the porous material.

show abstract

“…In the monolithic solution, Korsawe et al (2006) compared the Galerkin FEM with the Least-squares mixed FEM in order to verify which approaches are accurate and effective in the consolidation analysis. Extended mixed formulation based on hierarchical elements was also investigated by Rigobert et al (2003). However, the solutions for the impermeable and incompressible were not mentioned in the methods.…”

Section: Introductionmentioning

confidence: 99%

A new coupled analysis for nearly incompressible and impermeable saturated porous media on mixed finite element method: I. Proposed method

Park

Tak

2009

KSCE J Civ Eng

View full text Add to dashboard Cite

In the general mixed finite element analysis for the porous media, a fluid is assumed to be nearly incompressible; however, the solid may undergo a range of deformations from relatively large to small. If both constituent are assumed to be nearly incompressible and impermeable, the finite element analysis is very complex because of element locking. In order to overcome this difficulty, stable procedures using equal order elements have been introduced with stability analyses. However, these methods have a drawback that critical time steps in the stability analysis have to be determined by modal analysis. In this paper, a new coupled analysis based on a stable algorithm is introduced to remedy the drawback. First, governing equations for saturated porous media in frame of Biot's theory are derived on macroscopic sense, and that are represented into approximation forms which is divided into solid and fluid phase for finite element procedure. Moreover, a new coupled analysis based on a stable algorithm is introduced. In this procedure, the multi time step, the remeshing step and the sub iteration step are proposed for a stable analysis. These steps make it possible to simply solve numerical instabilities such as convergence and compatibility problems.

show abstract

Investigation of the convergence of the mixed displacement-pressure formulation for three-dimensional poroelastic materials using hierarchical elements

Cited by 39 publications

References 21 publications

Validity of the limp model for porous materials: A criterion based on the Biot theory

Validity of the limp model for porous materials: A criterion based on the Biot theory

On the influence of frequency-dependent elastic properties in vibro-acoustic modelling of porous materials under structural excitation

A new coupled analysis for nearly incompressible and impermeable saturated porous media on mixed finite element method: I. Proposed method

Contact Info

Product

Resources

About