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Description
This work revisits the linearized theory of micropolar elasticity for small deformations and presents a numerical implementation using mixed finite elements in the open-source software FEniCSx. Three boundary value problems are explored to showcase the physical implications of a micropolar formulation and give intuition to how the elastic parameters of the theory can relate to substructural effects on the microscale. A new analytical solution is derived for a two-dimensional shearing problem, incorporating forces and moment couples. This solution, as well as the well known analytical solution to the bending test for the state of pure bending, are used to gain an understanding of the elastic parameters in micropolar solids and to validate the numerical implementation. The torsion of a rectangular cuboid under rotational displacement boundary conditions is also examined numerically, demonstrating the characteristic micropolar effect of non-zero shear strain along the cuboid edges for a set of boundary conditions representative of those that might be prescribed in an experimental laboratory setting.
