A Parametrical Analysis on the Elastic Anisotropy of Woven Hierarchical Tissues

Abstract

AbstractIn this paper, the elastic properties of 2‐D woven hierarchical tissues are modeled, considering matrix transformation and stiffness averaging, assuming the warp and fill yarns (level 0) an orthotropic material. The tissue at level 1 is considered as the fabric composed of warp and fill yarns at level 0. Warp and fill yarns at level 1 are defined as “pieces” of such 1‐level tissue and have a different mismatch between the inclination of their longitudinal axes and those of the composing sub‐fibers. Similarly, based on warp and fill yarns at level 1, we generate warp and fill yarns at level 2 and thus tissues with two hierarchical levels, and so on. We compare our theory with experiments on tendons from the literature and on leaves performed by ourselves. The result shows the possibility of designing a new class of hierarchical 2‐D scaffolds by tailoring the elastic anisotropy, better matching the anisotropy of the biological tissues and thus maximizing their regeneration at each hierarchical level.