ArticleProceedings. Mathematical, physical, and engineering sciences2017
Effective equations governing an active poroelastic medium.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- Poroelasticity derived from the microstructure for intrinsically incompressible constituents.Zeitschrift fuer angewandte mathematik und physik · 2026Article
- Homogenized multiscale modelling of an electrically active double poroelastic material representing the myocardium.Biomechanics and modeling in mechanobiology · 2025Article
- Effective Governing Equations for Viscoelastic Composites.Materials (Basel, Switzerland) · 2023Article
- Investigating the effects of microstructural changes induced by myocardial infarction on the elastic parameters of the heart.Biomechanics and modeling in mechanobiology · 2023Article
- Effective Properties of Homogenised Nonlinear Viscoelastic Composites.Materials (Basel, Switzerland) · 2023Article
- Fracture of model end-linked networks.Proceedings of the National Academy of Sciences of the United States of America · 2022Article
- Regenerative medicine meets mathematical modelling: developing symbiotic relationships.NPJ Regenerative medicine · 2021Review
- Multiscale modelling and homogenisation of fibre-reinforced hydrogels for tissue engineering.European journal of applied mathematics · 2020Article
- A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation.Proceedings. Mathematical, physical, and engineering sciences · 2019Article
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4 authors.
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Abstract
In this work, we consider the spatial homogenization of a coupled transport and fluid-structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation and transport in an active poroelastic medium. The 'active' nature of the material results from a morphoelastic response to a chemical stimulant, in which the growth time scale is strongly separated from other elastic time scales. The resulting effective model is broadly relevant to the study of biological tissue growth, geophysical flows (e.g. swelling in coals and clays) and a wide range of industrial applications (e.g. absorbant hygiene products). The key contribution of this work is the derivation of a system of homogenized partial differential equations describing macroscale growth, coupled to transport of solute, that explicitly incorporates details of the structure and dynamics of the microscopic system, and, moreover, admits finite growth and deformation at the pore scale. The resulting macroscale model comprises a Biot-type system, augmented with additional terms pertaining to growth, coupled to an advection-reaction-diffusion equation. The resultant system of effective equations is then compared with other recent models under a selection of appropriate simplifying asymptotic limits.
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