Acceleration waves, flutter instabilities and stationary discontinuities in inelastic porous media

Loret, Benjamin; Harireche, Ouahid

doi:10.1016/0022-5096(91)90042-m

Cited by 54 publications

(32 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To interpret this condition, under dynamic loadings, one should compare it to the characteristic equation for acceleration wave speeds c as obtained in References [9,19] and which reads with the notations used here…”

Section: Loss Of Ellipticity Occurs If Non-trivial Solutions Of (87) mentioning

confidence: 98%

“…As pointed out also by experimental studies [5,6] the failure mechanism is in general strongly in uenced by the presence of the uid phase, and the physical time scale is important in the phenomenon. However, even though the di usion of the uid into the solid introduces a form of rate dependence, due to softening and (or) non-associativity in the skeleton rate-independent behaviour, the continuum rate problem may become ill-posed (see, for example, References [7,8] for one-phase materials, [9] for porous materials and [10,11] for porous materials under undrained conditions) with the classical numerical di culties and pathological mesh dependence of numerical results. Proper regularization is required and in the literature various approaches have been proposed and used in this speciÿc context of multi-phase materials.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On numerical analyses in the presence of unstable saturated porous materials

Benallal¹,

Comi²

2002

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYThe numerical analysis of the dynamic evolution problem concerning an elastic-plastic saturated porous media in the presence of softening (or non-associativity) is considered in the framework of the Biot formulation extended to take into account plastic phenomena. The ÿnite step boundary value problem, obtained by discretization in time of the continuous initial boundary value problem, is studied and the issue of its ill-posedness is particularly addressed. The conditions for the loss of ellipticity are established for the linearized problem solved at each iteration when using the Newton-Raphson scheme. In particular, the roles of the algorithmic properties on this loss of ellipticity are derived in details. The integration scheme of the balance of mass equation plays a major role and it is shown that the uid ow (Darcy's law) does indeed introduce a length scale but in addition to being dependent on the integration time step, it is found to be insu cient for regularization. To illustrate and corroborate the obtained results, a one-dimensional example (exhibiting all the features of the three-dimensional situation) is considered and the corresponding linearized ÿnite step problem is solved in closed form.

show abstract

Section: Loss Of Ellipticity Occurs If Non-trivial Solutions Of (87) mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

On numerical analyses in the presence of unstable saturated porous materials

Benallal¹,

Comi²

2002

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…The question therefore arises as to whether this finding should be considered as physically acceptable or as a consequence of inadequate modelling. The fact that a pore fluid may cause the flutter ill-posedness was mentioned in [5]. It was found that for a certain class of elasto-plastic models the flutter ill-posedness is excluded for a dry solid and is not excluded for a saturated solid.…”

Section: Introductionmentioning

confidence: 98%

“…Although the flutter type of ill-posedness has been extensively studied theoretically (e.g. [1,2,[5][6][7]9]), the question of its relevance to the real behaviour of solids still remains open. One might presume that pulsating or chaotic flow of granular materials observed in hoppers and silos could be a manifestation of dynamic ill-posedness.…”

Section: Introductionmentioning

confidence: 99%

On well-posedness of the dynamic problem for an anisotropic fluid-saturated solid

Osinov

2008

Arch Appl Mech

View full text Add to dashboard Cite

It is known that a high degree of anisotropy in the constitutive behaviour of a solid may result in the loss of hyperbolicity of the dynamic equations in the form of either complex-conjugate or purely imaginary characteristic wave speeds (flutter ill-posedness and shear band formation, respectively). In the present paper we investigate the characteristic wave speeds in the dynamic problem for a transversely isotropic fluid-saturated porous solid. Three cases are considered: a dry solid and a saturated solid under locally undrained and drained conditions. It is shown that, for given constitutive parameters of the solid skeleton, the dynamic problem for a drained solid may become ill-posed due to the flutter-type loss of hyperbolicity, while the dynamic equations for a dry and an undrained solids remain hyperbolic. For a given solid skeleton, the characteristic wave speeds are strongly influenced by the pore fluid compressibility which, in turn, is extremely sensitive to the presence of a small amount of free gas.

show abstract

“…Anand et al [12], and Zbib and Aifantis [13] conducted linear perturbation stability analyses for the onset of shear localization. Loret and Harireche [14] investigated the acceleration waves in inelastic porous media, and Benallal and Comi [15] showed material instabilities in saturated material under a dynamic state using a perturbation stability analysis. Oka et al [16] have been dealing with the strain localization problem of water-saturated clay through the use of viscoplastic constitutive equations because of the rate-dependent nature of cohesive soil.…”

mentioning

confidence: 99%

Stability Analysis of Methane Hydrate-Bearing Soils Considering Dissociation

et al. 2015

View full text Add to dashboard Cite

Abstract:It is well known that the methane hydrate dissociation process may lead to unstable behavior such as large ground deformations, uncontrollable gas production, etc. A linear instability analysis was performed in order to investigate which variables have a significant effect on the onset of the instability behavior of methane hydrate-bearing soils subjected to dissociation. In the analysis a simplified viscoplastic constitutive equation is used for the soil sediment. The stability analysis shows that the onset of instability of the material system mainly depends on the strain hardening-softening parameter, the degree of strain, and the permeability for water and gas. Then, we conducted a numerical analysis of gas hydrate-bearing soil considering hydrate dissociation in order to investigate the effect of the parameters on the system. The simulation method used in the present study can describe the chemo-thermo-mechanically coupled behaviors such as phase changes from hydrates to water and gas, temperature changes and ground deformation. From the numerical results, we found that basically the larger the permeability for water and gas is, the more stable the simulation results are. These results are consistent with those obtained from the linear stability analysis. OPEN ACCESSEnergies 2015, 8 5382

show abstract

Acceleration waves, flutter instabilities and stationary discontinuities in inelastic porous media

Cited by 54 publications

References 23 publications

On numerical analyses in the presence of unstable saturated porous materials

On numerical analyses in the presence of unstable saturated porous materials

On well-posedness of the dynamic problem for an anisotropic fluid-saturated solid

Stability Analysis of Methane Hydrate-Bearing Soils Considering Dissociation

Contact Info

Product

Resources

About