Effective equations for fluid-structure interaction with applications to poroelasticity

Brown, Donald L.; Popov, Peter; Efendiev, Yalchin

doi:10.1080/00036811.2013.839780

Cited by 31 publications

(55 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To permit analysis, the authors of [54,61] (and other similar studies) exploited asymptotic restrictions on the underlying model, considering slow (quasi-static) growth and linearised deformation. Collis et al [17] relaxed such assumptions to consider a macroscale representation of finite volumetric nutrient-limited growth of a hyperelastic solid, employing the arbitrary Lagrangian-Eulerian approach [12] to ameliorate the challenges involved in applying two-scale asymptotics to such a system.…”

Section: Introductionmentioning

confidence: 99%

A Multiphase Multiscale Model for Nutrient Limited Tissue Growth

Holden¹,

Collis²,

Brook³

et al. 2018

ANZIAM J.

View full text Add to dashboard Cite

We derive an effective macroscale description for the growth of tissue on a porous scaffold. A multiphase model is employed to describe the tissue dynamics; linearisation to facilitate a multiple-scale homogenisation provides an effective macroscale description, which incorporates dependence on the microscale structure and dynamics. In particular, the resulting description admits both interstitial growth and active cell motion. This model comprises Darcy flow, and differential equations for the volume fraction of cells within the scaffold and the concentration of nutrient, required for growth. These are coupled with Stokes-type cell problems on the microscale, incorporating dependence on active cell motion and pore scale structure. The cell problems provide the permeability tensors with which the macroscale flow is parameterised. A subset of solutions is illustrated by numerical simulations.

show abstract

Section: Introductionmentioning

confidence: 99%

A Multiphase Multiscale Model for Nutrient Limited Tissue Growth

Holden¹,

Collis²,

Brook³

et al. 2018

ANZIAM J.

View full text Add to dashboard Cite

show abstract

“…Although, in this paper, we do not describe behaviour at the pore level, the proposed formulation is coherent with the homogenization procedure which can provide the desired effective material parameters at the deformed configuration. In relationships with existing works [39,37] and [11], this is an important aspect which justifies the proposed formulation as an improved modelling framework for a more accurate multi-scale computational analysis of the porous media.…”

Section: Introductionmentioning

confidence: 71%

Modeling large-deforming fluid-saturated porous media using an Eulerian incremental formulation

Rohan

Lukeš

2017

Advances in Engineering Software

View full text Add to dashboard Cite

The paper deals with modelling fluid saturated porous media subject to large deformation. An Eulerian incremental formulation is derived using the problem imposed in the spatial configuration in terms of the equilibrium equation and the mass conservation. Perturbation of the hyperelastic porous medium is described by the Biot model which involves poroelastic coefficients and the permeability governing the Darcy flow. Using the material derivative with respect to a convection velocity field we obtain the rate formulation which allows for linearization of the residuum function. For a given time discretization with backward finite difference approximation of the time derivatives, two incremental problems are obtained which constitute the predictor and corrector steps of the implicit time-integration scheme. Conforming mixed finite element approximation in space is used. Validation of the numerical model implemented in the SfePy code is reported for an isotropic medium with a hyperelastic solid phase. The proposed linearization scheme is motivated by the two-scale homogenization which will provide the local material poroelastic coefficients involved in the incremental formulation.

show abstract

“…We will now consider nonlinear solve in space after time discretization by the fully coupled scheme (7). One could rewrite (7) as a nonlinear system each time step and use a Newton solver, however, for our GMsFEM we prefer to use a linearization based on Picard iteration.…”

Section: Fine-scale Discretizationmentioning

confidence: 99%

A generalized multiscale finite element method for poroelasticity problems II: Nonlinear coupling

Brown

Vasilyeva

2016

Journal of Computational and Applied Mathematics

Self Cite

View full text Add to dashboard Cite

In this paper, we consider the numerical solution of some nonlinear poroelasticity problems that are of Biot type and develop a general algorithm for solving nonlinear coupled systems. We discuss the difficulties associated with flow and mechanics in heterogenous media with nonlinear coupling. The central issue being how to handle the nonlinearities and the multiscale scale nature of the media. To compute an efficient numerical solution we develop and implement a Generalized Multiscale Finite Element Method (GMsFEM) that solves nonlinear problems on a coarse grid by constructing local multiscale basis functions and treating part of the nonlinearity locally as a parametric value. After linearization with a Picard Iteration, the procedure begins with construction of multiscale bases for both displacement and pressure in each coarse block by treating the staggered nonlinearity as a parametric value. Using a snapshot space and local spectral problems, we construct an offline basis of reduced dimension. From here an online, parametric dependent, space is constructed. Finally, after multiplying by a multiscale partitions of unity, the multiscale basis is constructed and the coarse grid problem then can be solved for arbitrary forcing and boundary conditions. We implement this algorithm on a geometry with a linear and nonlinear pressure dependent permeability field and compute error between the multiscale solution with the fine-scale solutions.

show abstract

Effective equations for fluid-structure interaction with applications to poroelasticity

Cited by 31 publications

References 9 publications

A Multiphase Multiscale Model for Nutrient Limited Tissue Growth

A Multiphase Multiscale Model for Nutrient Limited Tissue Growth

Modeling large-deforming fluid-saturated porous media using an Eulerian incremental formulation

A generalized multiscale finite element method for poroelasticity problems II: Nonlinear coupling

Contact Info

Product

Resources

About