Size-independent strain gradient effective models based on homogenization methods: Applications to 3D composite materials, pantograph and thin walled lattices

The notion of strain gradients provides a reliable model for capturing size effects and localization phenomena. The difficulty in identifying corresponding constitutive parameters, on the other hand, restricts the practical applicability of such theory. In this work, we aim at developing homogenization based strain-gradient continuum models to compute the effective Cauchy and strain gradient moduli for a wide class of 3D architectured materials and composites prone to strain gradient effects. The present homogenization method is based on a variational principle in linear elasticity articulated with Hill's lemma, which is extended by considering the generalized kinematics within the framework of periodic homogenization. The microscopic displacement field is decomposed into a polynomial function of the introduced macroscopic kinematic variables and the other is periodic fluctuation. The fluctuating displacement is expressed versus the macroscopic kinematic variables solving sequential classical and higher order unit cell boundary value problems. The computed effective elastic moduli in the current computing framework do not depend on the unit cell size, and are therefore intrinsic to the microstructure within the structure. 3D applications for inclusion based composites, pantographic lattices and thin-walled lattice structures showing pronounced strain gradient effects are carried out in order to exemplify the proposed homogenization strategy.