Geometric nonlinear mechanical behavior of anisotropic materials as Cosserat continua

The non-local effect related to microstructures has become increasingly significant in materials like lightweight concrete and honeycombs. Most of such composite materials and structures result in having a nonlinear behavior under applied loads, necessitating advanced computational methods. This study investigates the geometrically nonlinear behavior of anisotropic microstructured materials using a total Lagrangian finite element formulation for the Cosserat continuum. Equivalent anisotropic properties are derived by homogenizing composites featuring different hexagonal microstructural geometries. By analyzing a 2D cantilever beam problem, the nonlinear Cosserat model is compared against the Cauchy continuum and linear versions. Results demonstrate that geometric nonlinear models provide a more realistic description of mechanical responses, particularly under large deformations where linear models prove inadequate. A significant micropolar scale effect is identified on the geometric nonlinear behavior: while Cosserat and Cauchy models converge at small scales, they diverge as the microstructure scale increases relative to the macro scale. Furthermore, different anisotropic configurations exhibit unique load–displacement characteristics, ranging from slightly to highly nonlinear. Although the Cosserat implementation requires higher computational effort than the Cauchy model, this work highlights its value in accurately capturing the non-local features and scale effects inherent in the geometric nonlinear behavior of microstructured composites. • Total Lagrangian FEM for geometrically nonlinear anisotropic Cosserat continua. • Cosserat model yields lighter geometric nonlinearity than the Cauchy model. • Geometric nonlinearity by Cosserat model weakens as microstructure’s scale increases. • Computational effort for the Cosserat model correlates with geometric nonlinearity.