Abstract:

Growth is a complex process that can be widely and easily observed in nature and technology. Elastic growth models have been developed over nearly a half century to describe certain evolution behavior of biological systems. Here, we will report an analytical investigation of the growth of a cylindrical core constrained in two surface cylindrical layers. Both the surface cylindrical layers and the inner core are assumed to be nonlinear elastic and isotropic, for which a nonlinear constitutive relation accommodating elastic growth is adopted. Analytical expressions are derived and numerical calculations are performed. It is shown that, due to the different growth rates of the core and the surface layers, residual stress field will be created in the laminated structure, which in turn leads to an equivalent and macroscopic material inhomogeneity and anisotropy. Thus, this simple model can be used to interpreting the unique material behavior of bamboo.