Homogenization of a system of elastic and reaction-diffusion equations modelling plant cell wall biomechanics

Mariya Ptashnyk, Brian Seguin

Research output: Contribution to journalArticle

9 Citations (Scopus)


In this paper we present a derivation and multiscale analysis of a mathematical model for plant cell wall biomechanics that takes into account both the microscopic structure of a cell wall coming from the cellulose microfibrils and the chemical reactions between the cell wall's constituents. Particular attention is paid to the role of pectin and the impact of calcium-pectin cross-linking chemistry on the mechanical properties of the cell wall. We prove the existence and uniqueness of the strongly coupled microscopic problem consisting of the equations of linear elasticity and a system of reaction-diffusion and ordinary differential equations. Using homogenization techniques (two-scale convergence and periodic unfolding methods) we derive a macroscopic model for plant cell wall biomechanics.

Original languageEnglish
Pages (from-to)593-631
Number of pages39
JournalESAIM: Mathematical Modelling and Numerical Analysis
Issue number2
Publication statusPublished - Mar 2016


  • Elasticity
  • Homogenization
  • Periodic unfolding method
  • Plant modelling
  • Reaction-diffusion equations
  • Two-scale convergence

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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