Modelling of laminated growing biological materials

Abstract

The continued model of the multilayered plate from a growing biological material is presented. Introducing the Airy's stress function the problem is reduced to differential equation of the fourth order. Solution of the problem is obtained for the two- layered plate with a rectangle cross-section. For some relations between the rheological coefficients of the model the governing equations are simplified and the corresponding theoretical estimations are obtained. Numerical calculations of the stress and velocity fields for the model parameters that correspond to the growing plant leaves are presented. Any difference in own growth rates of the adjacent layers leads to stretching of the tempered layer and compressing of the rapidly growing one that results in growth acceleration of the former and growth retardation of the latter. Thus the mechanical stress field can regulate coordinated growth of the laminated biological materials.