Studies of microstructural size effect and higher-order deformation in second-order computational homogenization

Two examples illustrating microstructural size effect and higher-order deformation are considered within the context of second-order computational homogenization. Governing equations and appropriate discretization are briefly reviewed, including the scale transition equations and the enforcement of generalised boundary conditions for the RVE (representative volume element). The first example serves as a means of validation for second-order computational homogenization and highlights the difference in terms of higher-order deformation of the RVE between the first and second-order schemes. The second example (indentation test) focuses on microstructural size effect, whereby the result is shown to be dependent on the intrinsic length of the RVE.