On the effective stress law and its application to finite deformation problems in a poroelastic solid

Zheng, Pei; Zhang, Keming

doi:10.1016/j.ijmecsci.2019.105074

Cited by 12 publications

(5 citation statements)

References 39 publications

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“…Histological studies based on diffusion tensor imaging indicate a fibre architecture that rotates 120 • from the epicardial to the endocardial surface. A volumetric part of the energy is added for the case of nearly incompressible materials, for example, the term U (J ) = 1 2 λ s (ln J ) 2 (with λ s another material parameter) which is designed to enforce convexity or polyconvexity of the strain density [85].…”

Section: Continuum Model and Proposed Set Of Field Equationsmentioning

confidence: 99%

Finite Element Methods for Large-Strain Poroelasticity/Chemotaxis Models Simulating the Formation of Myocardial Oedema

Gómez-Vargas

Lourenço

et al. 2022

J Sci Comput

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In this paper we propose a novel coupled poroelasticity-diffusion model for the formation of extracellular oedema and infectious myocarditis valid in large deformations, manifested as an interaction between interstitial flow and the immune-driven dynamics between leukocytes and pathogens. The governing partial differential equations are formulated in terms of skeleton displacement, fluid pressure, Lagrangian porosity, and the concentrations of pathogens and leukocytes. A five-field finite element scheme is proposed for the numerical approximation of the problem, and we provide the stability analysis for a simplified system emanating from linearisation. We also discuss the construction of an adequate, Schur complement based, nested preconditioner. The produced computational tests exemplify the properties of the new model and of the finite element schemes.

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Section: Continuum Model and Proposed Set Of Field Equationsmentioning

confidence: 99%

Finite Element Methods for Large-Strain Poroelasticity/Chemotaxis Models Simulating the Formation of Myocardial Oedema

Gómez-Vargas

Lourenço

et al. 2022

J Sci Comput

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“…Histological studies based on diffusion tensor imaging indicate a fibre architecture that rotates 120 • from the epicardial to the endocardial surface. A volumetric part of the energy is added for the case of nearly incompressible materials, for example, the term U (J) = 1 2 λ s (lnJ) 2 (with λ s another material parameter) which is designed to enforce convexity or polyconvexity of the strain density [78].…”

Section: Continuum Model and Proposed Set Of Field Equationsmentioning

confidence: 99%

Finite element methods for large-strain poroelasticity/chemotaxis models simulating the formation of myocardial oedema

Nicolas¹,

Gómez-Vargas²,

Lourenço³

et al. 2021

Preprint

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In this paper we propose a novel coupled poroelasticity-diffusion model for the formation of extracellular oedema and infectious myocarditis valid in large deformations, manifested as an interaction between interstitial flow and the immune-driven dynamics between leukocytes and pathogens. The governing partial differential equations are formulated in terms of skeleton displacement, fluid pressure, Lagrangian porosity, and the concentrations of pathogens and leukocytes. A five-field mixed-primal finite element scheme is proposed for the numerical approximation of the problem, and we provide the stability analysis for a simplified system emanating from linearisation. We also discuss the construction of an adequate, Schur complement based, nested preconditioner. The produced computational tests exemplify the properties of the new model and of the mixed schemes.

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“…It is observed that the stretch λ 2 at the boundary ξ = 1 evolves with time, as expected, and eventually reaches its steady-state value λ 2 = 1 . 444 at the long-time limit. In the steady state, it is noticed that a nonuniform porosity distribution is achieved in the cylindrical tube, unlike in the case of a one-dimensional configuration, say, a finite porous layer (see [39]), and that the porosity change decreases monotonically with increasing ξ . The time history of the applied mechanical pressure computed from equation (99) is plotted as the blue line in Figure 3(a).…”

Section: Numerical Examplesmentioning

confidence: 99%

Nonlinear magnetoelastic deformations of porous solids

Zheng

Tang

Ding

2021

Mathematics and Mechanics of Solids

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A magnetoactive porous solid comprises a porous polymer matrix with embedded magnetizable particles. The connected porous space of the polymer matrix is filled with a fluid. Under externally applied magnetic fields, the magnetoactive porous solid can undergo large deformations in the elastic regime, triggering diffusive flow in the interconnected pores. The coupled hydromagnetomechanical behavior of such materials has recently received considerable attention. In this paper, the effective stress principle is applied to the constitutive modeling of the material at finite strains. In contrast to previous works, the Lagrangian porosity is no longer treated as an independent constitutive variable in the proposed formulation. To investigate the effect of the magnetic field on the mechanical response of the material, as well as to illustrate the theory, the problem of inflation of a circular cylindrical tube in the presence of a uniform axial magnetic field is formulated and solved. Computational results are presented graphically.

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On the effective stress law and its application to finite deformation problems in a poroelastic solid

Cited by 12 publications

References 39 publications

Finite Element Methods for Large-Strain Poroelasticity/Chemotaxis Models Simulating the Formation of Myocardial Oedema

Finite Element Methods for Large-Strain Poroelasticity/Chemotaxis Models Simulating the Formation of Myocardial Oedema

Finite element methods for large-strain poroelasticity/chemotaxis models simulating the formation of myocardial oedema

Nonlinear magnetoelastic deformations of porous solids

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