The strain energy function of an ideal plant cell wall

Most plant cells are surrounded by a rigid cell wall composed of many cellulose microfibrils embedded in a matrix. By taking up water from their environment, a strong hydrostatic force which pushes against the cell wall is created. Throughout this paper it will be assumed that growth occurs when this force exceeds the wall strength, stretching the fibres apart and allowing the wall to expand. Both the matrix and the microfibrils have polymer structures and this lends a description of cell wall expansion to be made in terms of non-linear elasticity principles. This theory naturally allows for large deformations of the type exhibited in plant cell wall expansion. By describing the elastic properties of the cell wall in terms of a strain energy function the two phases of cell wall expansion (i.e. the matrix-regulated phase and the microfibril-regulated phase) can be accurately modelled. Pressure-volume relationships for ideal polymer spherical and cylindrical shells are derived and the results are compared qualitatively with actual experimental pressure-volume relationships obtained from the literature.