A few remarks on Biot's model and linear acoustics of poroelastic saturated materials

Wilmanski, Krzysztof

doi:10.1016/j.soildyn.2006.01.006

Cited by 60 publications

(52 citation statements)

References 34 publications

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“…Note that a comparable relation of the porosity can also be found for the fully compressible model of Biot as pointed out in a recent contribution [40]. Wilmański's porosity balance for the linear compressible model can be also discussed for the rigid grain limit…”

Section: Kinematical Assumptionssupporting

confidence: 53%

“…As remarked earlier in this contribution, this could only be achieved by a more realistic physically based approach for the non-equilibrium momentum interaction (inertia coupling), cf. the remarks in a recent work of Wilmański [40]. In the low-frequency range, viscous coupling locks the bone matrix and the bone marrow and prevents a travelling slow wave.…”

Section: Effective Stress Of the Solid Skeletonmentioning

confidence: 92%

“…Thus, the evolution of porosity φ(x, t) depends only on the volumetrical deformation of the solid and the liquid constituent, cf. Wilmański [40]. The microscopical basis of the porosity is the pore size and its distribution which is only represented in an averaged sense in such theories.…”

Section: Introductionmentioning

confidence: 99%

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Ultrasound propagation in cancellous bone

Steeb

2009

Arch Appl Mech

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Wave propagation in fluid-saturated cancellous bone is studied on the basis of two approaches: The thermodynamic-consistent Theory of Porous Media (TPM) and Biot's theory. Phase velocities in the lowfrequency range, calculated with the Biot-Gassmann relations, Wyllie's equation and the TPM, are demonstrating that a simple, so-called hybrid biphasic TPM model is able to capture the main acoustical effects in cancellous bones. Furthermore, an extension towards high-frequency wave propagation is discussed on the basis of the constitutive relations for the momentum exchange of the fluid and the solid phases. Further numerical results show that, in the high-frequency (ultrasound) range a viscous correction as well as an added mass effect (tortuosity) needs to be taken into account to explain experimentally obtained results.

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Section: Kinematical Assumptionssupporting

confidence: 53%

Section: Effective Stress Of the Solid Skeletonmentioning

confidence: 92%

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Ultrasound propagation in cancellous bone

Steeb

2009

Arch Appl Mech

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“…This makes it possible to match the additive stress decomposition (effective stress plus pore pressure) with the multiplicative decomposition of the deformation gradient (instead of the additive strain decomposition adopted in small-strain theory). In contrast with Wilmanski (2006), the free energy proves to be a potential for the stresses in the solid and fluid phases, and-extending Biot's linear theory-the volume fractions are obviously not considered constant. As a by-product, the proposed method provides the extension to large strains of the effective stress formulated by Nur & Byerlee (1971) for small strains and compressible solid constituents.…”

Section: Introductionmentioning

confidence: 99%

A general approach to isothermal hyperelastic modelling of saturated porous media at finite strains with compressible solid constituents

Gajo

2010

Proc. R. Soc. A.

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A general approach is proposed for defining the macroscopic free-energy function of a saturated porous medium subjected to finite deformations, under isothermal conditions, in the case of compressible fluid and solid constituents. Reference is made to an elementary volume treated as an 'open system', moving with the solid skeleton. The strain-like variables are characterized by a suitable strain measure and the variation of fluid-mass content. Although the free energy is obtained by assembling the contributions of the single constituents, the resulting free energy is not the simple sum of the free energies of the single constituents. It is shown that the simplified approaches previously proposed in the literature are recovered as particular cases of the more general framework proposed in the present article and, in addition, new simplified constitutive frameworks are investigated. The proposed approach paves the way to the consistent hyperelasticplastic and thermo-elastic modelling of saturated porous media with compressible fluid and solid constituents.

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“…Following [28], we consider the case α ≈ 1, B ≈ 1, K u → ∞ and a linear dependence between the fluid pressure and the pore pressure, p l = (1 − φ)p [30]. Furthermore, we assume that the coupling is instantaneous.…”

Section: Incompressibility Conditionsmentioning

confidence: 99%

A 2D Computational Model of Lymphedema and of its Management with Compression Device

Eymard

Volpert

Quéré

et al. 2017

Math. Model. Nat. Phenom.

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Abstract. The purpose of this study is to model a lymphedema following a mastectomy and its management (compression therapy). During surgery for breast cancer, an axillary node dissection can be done and cause damages to the lymphatic system leading to a secondary lymphedema located in upper limb. Limb lymphedema is an incurable disease associated with chronic and progressive limb swelling condition. The main clinical consequence of lymphedema is the limb edema, clinically resulting in pain, discomfort, strength reduction and musculoskeletal complications due to limb excessive heaviness. Some devices for lymphedema (e.g. bandaging and garments) could be more personalized, taking into account both characteristics of compressions and patients. Before the evaluation of these therapeutic strategies in humans, an "in silico" approach could be used to investigate the interest of gradual or intermittent compression testing in virtual patients. For that purpose, we developed a simplified model of the lymph flow through the lymphatic system in a whole upper limb including the corresponding interstitial fluid exchanges.

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A few remarks on Biot's model and linear acoustics of poroelastic saturated materials

Cited by 60 publications

References 34 publications

Ultrasound propagation in cancellous bone

Ultrasound propagation in cancellous bone

A general approach to isothermal hyperelastic modelling of saturated porous media at finite strains with compressible solid constituents

A 2D Computational Model of Lymphedema and of its Management with Compression Device

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