Homogenization of Biomechanical Models for Plant Tissues

DOI10.1137/15M1046198zbMath1383.35019arXiv1509.00387OpenAlexW1949653435MaRDI QIDQ5737755

Mariya Ptashnyk, Andrey L. Piatnitski

Publication date: 30 May 2017

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.00387

zbMATH Keywords

homogenizationStokes systemtwo-scale convergenceporoelasticityperiodic unfolding methodbiomechanics of plant tissues

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Biomechanics (92C10) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Plant biology (92C80)

Related Items (9)

Multiscale modelling and homogenisation of fibre-reinforced hydrogels for tissue engineering ⋮ Influence of asymptotically-limiting micromechanical properties on the effective behaviour of fibre-supported composite materials ⋮ Smoothed particle hydrodynamics for root growth mechanics ⋮ Homogenization of a spherical harmonics expansion model ⋮ Homogenization of biomechanical models of plant tissues with randomly distributed cells ⋮ Stochastic Unfolding and Homogenization of Spring Network Models ⋮ Strain gradient nonlocal Biot poromechanics ⋮ Simulating the temporal change of the active response of arteries by finite elements with high-order time-integrators ⋮ Localization and multiplicity in the homogenization of nonlinear problems

Cites Work

• Coupling Biot and Navier-Stokes equations for modelling fluid-poroelastic media interaction
• Invariant sets for strongly coupled reaction-diffusion systems under general boundary conditions
• On propagation of acoustic waves in the medium consisting of a fluid and an elastic material
• Non-homogeneous media and vibration theory
• Propagation of waves in a fluid-saturated porous elastic solid
• Homogenization of reticulated structures
• Homogenizing the acoustic properties of the seabed. I
• Diffusion in poro-elastic media
• Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach
• Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics
• The Periodic Unfolding Method in Domains with Holes
• Homogenization Limit of a Model System for Interaction of Flow, Chemical Reactions, and Mechanics in Cell Tissues
• Asymptotic Analysis for a Stiff Variational Problem Arising in Mechanics
• The existence and uniqueness theorem in Biot's consolidation theory
• Poroelasticity equations derived from microstructure
• L^PBounds of solutions of reaction-diffusion equations
• An extension theorem from connected sets, and homogenization in general periodic domains
• Homogenization and Two-Scale Convergence
• A General Convergence Result for a Functional Related to the Theory of Homogenization
• On an extension of the method of two-scale convergence and its applications
• ON THE INTERFACE LAW BETWEEN A DEFORMABLE POROUS MEDIUM CONTAINING A VISCOUS FLUID AND AN ELASTIC BODY
• Micromechanical computational modeling of secondary consolidation and hereditary creep in soils.
• Homogenizing the acoustic properties of the seabed. II.
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