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

TL;DR

This paper develops a multiscale mathematical model for plant cell wall biomechanics, incorporating microscopic structure and chemical reactions, and derives a macroscopic model through homogenization techniques.

Contribution

It presents a homogenization approach for coupled elastic and reaction-diffusion equations modeling plant cell walls, including chemical effects like calcium-pectin cross-linking.

Findings

Existence and uniqueness of the microscopic problem proved.

Derivation of a macroscopic model via homogenization methods.

Insights into the role of chemical reactions in mechanical properties.

Abstract

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.