Computational Analysis of the Size Effects Displayed in Beams with Lattice Microstructures

Abstract

The mechanical behaviour of finite element based computational representations of heterogeneous materials with regular or periodic cellular microstructure is compared to existing closed form analytical predictions of their constitutive behaviour available within the open literature. During the computational investigation, slender, geometrically similar rectangular beams of different sizes which are comprised of regular, repeating arrangements of square cellular microstructures were represented using the finite element analysis (FEA) software ANSYS. Flexural loading of the virtual samples reveals that the materials exhibit the theoretically forecast size effect from which the relevant material constitutive properties, notably the flexural modulus and characteristic length can be identified. Initial findings suggest that while there is agreement between the numerically determined and theoretically predicted moduli the characteristic lengths in bending, $l_b$, calculated from the numerical data appear to differ from the theoretical forecasts. Moreover, the computational representations indicate that finite sized material samples are capable of exhibiting size effects not predicted by the more general higher order constitutive theories. Results indicate that the nature of the size effect appears to depend on the prescription of the sample surfaces with respect to the specified microstructure of the material. While these unanticipated size effects show qualitative agreement with that forecast for a simple laminate material comprised of alternating stiff and compliant layers the consequences may be profound for experimental mechanical testing of such materials.