Heterogeneity and anisotropy are two important features of biological materials, such as bone in animals, trunk of wood, and culm of bamboo. Both material heterogeneity and anisotropy have their particular biological functions and are formed through a complex and systematic biochemical process. In this paper, we intend to use a simple mechanical theory—the elastic growth theory—to predict these two features that are widely observed in bamboo. The theory assumes that the deformation gradient tensor is composed of two parts: one related to volumetric growth and the other corresponding to deformation. The analysis is carried out for a two-layered hollow cylinder model, which captures the main geometric characteristic of the cross-section of bamboo culm. Though the problem is nonlinear, we are able to derive exact and explicit expressions for the stresses and displacements in both layers. It is shown that, due to the volumetric growth, a residual stress field and elastic deformation are induced in the structure, which in turn leads to an equivalent and macroscopic material gradient and anisotropy. Numerical examples are considered to confirm the validity of the theoretical model and to perform a parametric study.
Acta Mechanica – Springer Journals
Published: Dec 26, 2015
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