Parallel Krylov methods and the application to 3-d simulations of a triphasic porous media model in soil mechanics

Wieners, Christian; Graf, Thomas; Ammann, M.; Ehlers, Wolfgang

doi:10.1007/s00466-004-0654-1

Cited by 14 publications

(4 citation statements)

References 13 publications

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“…The first one, as a fundamental geotechnical problem, concerns the mechanics of unsaturated soil, while the second one describes the possibilities of electro-active polymers and gels and can easily be reduced to swelling phenomena of active soil and biological tissue. Various further applications can be taken from the literature [8,37,43,60,61] and from the work of the author and coworkers, cf. e.g.…”

Section: General Frameworkmentioning

confidence: 99%

Challenges of porous media models in geo- and biomechanical engineering including electro-chemically active polymers and gels

Ehlers

2009

Int J Adv Eng Sci Appl Math

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Miscible multi-component materials like classical mixtures as well as immiscible materials like saturated and partially saturated porous media can be successfully described on the common basis of the well-founded Theory of Mixtures (TM) or the Theory of Porous Media (TPM). In particular, both the TM and the TPM provide an excellent framework for a macroscopic description of a broad variety of applications ranging, for example, from standard and sophisticated problems in geomechanics via biomechanical applications to electro-chemically active polymers and gels, etc. The present article portrays general multiphasic and multi-component materials, thus reflecting their mechanical and their thermodynamical framework, while furthermore adding electro-chemical effects. Including some constitutive models and illustrative numerical examples, the article can be understood as a reference to theoretical and numerical investigations in the broad field of porous media models.

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Section: General Frameworkmentioning

confidence: 99%

Challenges of porous media models in geo- and biomechanical engineering including electro-chemically active polymers and gels

Ehlers

2009

Int J Adv Eng Sci Appl Math

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“…solve K x = r −t (31c) For the solution of the two linear subproblems (31a) and (31b) we use a parallel Krylov method [41] accelerated with a multilevel ILU preconditioner with pivoting and dropping strategy by…”

Section: Solution Of the Linearized Systemmentioning

confidence: 99%

Numerical approximation of incremental infinitesimal gradient plasticity

Neff

Sydow

Wieners

2008

Numerical Meth Engineering

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We investigate a representative model of continuum infinitesimal gradient plasticity. The formulation is an extension of classical rate‐independent infinitesimal plasticity based on the additive decomposition of the symmetric strain tensor into elastic and plastic parts. It is assumed that dislocation processes contribute to the storage of energy in the material whereby the curl of the plastic distortion appears in the thermodynamic potential and leads to an additional nonlocal backstress tensor. The formulation is cast into a numerical framework by a saddle point approximation of the corresponding minimization problem in each incremental loading step. This allows one to reformulate the (nonlocal) dissipation inequality to a point‐wise flow rule and yields a solution scheme, which is a direct extension of the standard approach in classical plasticity. Our numerical results show the regularizing effects of the additional physically motivated terms. Copyright © 2008 John Wiley & Sons, Ltd.

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“…This approach provides an ideal framework for multiphasic and multicomponent continua including arbitrary solid deformations based on elasticity, viscoelasticity, or elastoplasticity, as well as an arbitrary pore content of either miscible or immiscible fluids, liquids and gases. The reader who is interested in the basics of the TPM is referred, for example, to the publications of de Boer (2000), de Boer and Ehlers (1986), Bowen (1980Bowen ( , 1982, Ehlers (1991Ehlers ( , 1989Ehlers ( , 2002, Ehlers et al (2004), Wieners et al (2005), Ehlers and Graf (2007), Ehlers (2009) or Schrefler and Zhan (1993), Schrefler and Scotta (2001), and citations therein.…”

Section: Introductionmentioning

confidence: 99%

Interfacial Mass Transfer During Gas–Liquid Phase Change in Deformable Porous Media with Heat Transfer

Ehlers

Häberle

2016

Transp Porous Med

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Transitions between liquid and gaseous phases of a fluid material are characterised by a jump in density and the coexistence of both phases during the phase change process. The jump occurs at the interface between the fluid phases and can be handled numerically by the introduction of a singular surface. This allows for a thermodynamically consistent description of mass transfer across the interface and the transition of the interfacial term towards the mass production term included in the mass balance equations. In the present article, a multicomponent and multiphasic porous aggregate is treated in a non-isothermal environment, while accounting for the thermodynamics of the fluid-phase transitions. Based on the Theory of Porous Media, this approach provides a well-founded continuum mechanical basis for the description of deformable, fluid-saturated porous solid aggregates. In particular, a bicomponent, triphasic model is proposed consisting of a thermoelastic porous solid, which is percolated by compressible gaseous and liquid fluid phases. The thermodynamical behaviour, i.e. the dependency of the fluid densities on temperature and pressure, is governed by the van der Waals equation of state and the Antoine equation for the vaporisation-condensation line. Moreover, the interface between the fluid phases is represented by a singular surface and results in jump conditions included in the balance relations of the components of the overall aggregate. The evaluation of the jump conditions leads to a formulation of the interfacial mass transfer, which basically relates the energy added to the system to the latent heat needed for the phase change in a certain amount of a substance. The mass transfer itself or the mass production, respectively, furthermore depends on interfacial areas introduced as a function of

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Parallel Krylov methods and the application to 3-d simulations of a triphasic porous media model in soil mechanics

Cited by 14 publications

References 13 publications

Challenges of porous media models in geo- and biomechanical engineering including electro-chemically active polymers and gels

Challenges of porous media models in geo- and biomechanical engineering including electro-chemically active polymers and gels

Numerical approximation of incremental infinitesimal gradient plasticity

Interfacial Mass Transfer During Gas–Liquid Phase Change in Deformable Porous Media with Heat Transfer

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