Finite Gradient Models with Enriched RBF-Based Interpolation

A finite strain gradient model for the 3D analysis of materials containing spherical voids is presented. two-scale approach proposed: a least-squares methodology RVE with quadratic displacements and full high-order continuum both fourth-order sixth-order elasticity tensors. meshless method adopted using radial basis function interpolation polynomial enrichment. Both first second derivatives resulting shape functions are described in detail. Complete expressions deformation F its ?F derived consistent linearization performed to ensure Newton solution. total seven constitutive properties required. The classical Lamé parameters corresponding pristine material considered constant. From homogenization, obtained, two homogenized plus five gradient-related properties. Two validation numerical examples example exhibits size effect (i.e., stiffening smaller specimens) shows absence stress singularity hence convergence discretization method.