Analysis of surface effects based on first and second strain gradient mechanics

Abstract

The present contribution provides an analysis of surface effects in the mechanical response of architected materials modeled in the framework of strain gradient mechanics. The classical and strain gradient properties are evaluated by relying on a dedicated discrete homogenization method to upscale the microstructural information towards an effective strain gradient continuum at the macroscopic level. The formulation of the strain gradient model formulated via Hill extended macrohomogeneity condition allows a proper surface expression of the effective strain gradient kinematic and static variables. The scaling law of the strain gradient moduli with the edge contribution is obtained from their closed-form expressions versus the lattice microstructural parameters, and recoursing to the notion of shape derivative. The sensitivity of the strain gradient moduli to the relative amount of bulk versus surface effects is evaluated, showing that absolute size effects are well captured by strain gradient moduli. The energetic formulation of a second strain gradient continuum allows to revisit the notion of anisotropic surface energy, thereby providing a generalization of Mindlin's model (Mindlin, 1965) of surface energy.