Characteristic lengths in natural bundle assemblies arising from fiber-matrix energy competition: A floquet-based homogenization theory

摘要: Abstract The physical heterogeneity and the geometrical periodicity of several bundle architectures found in biological materials play a key role determining their superior mechanical performances. underlying mechanism is based on shear stress transfer between hard fibers soft matrix. This process yields size-dependent behavior characterized by specific lengths scales. Here, we elaborate Floquet-based homogenization valid for arbitrary periodically heterogeneous fiber bundles with subject to mutual interactions. approach allows us separately evaluate energy distribution within matrix, define an efficiency function able optimize response bundle. We show existence characteristic length scale that maximizes elastic from thus reducing solicitation enhancing overall response. theory describe features biomaterials, such as nacre shell, muscle sarcomere, collagen fibril, spider silk, excellent agreement experimental data. Moreover, it can be used design bioinspired artificial structures optimal