Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme

Abstract A gradient‐enhanced computational homogenization procedure, that allows for the modelling of microstructural size effects, is proposed within a general non‐linear framework. In this approach the macroscopic deformation gradient tensor and its gradient are imposed on a microstructural representative volume element (RVE). This enables us to incorporate the microstructural size and to account for non‐uniform macroscopic deformation fields within the microstructural cell. Every microstructural constituent is modelled as a classical continuum and the RVE problem is formulated in terms of standard equilibrium and boundary conditions. From the solution of the microstructural boundary value problem, the…