As a first step, variational formulations and governing equations with boundary conditions
are derived for a pair of Euler–Bernoulli beam bending models following a simplified version …

For three-dimensional cellular plate-like structures with a triangular (extruded lattice)
microarchitecture, the article develops a pair of two-scale plate models relying on the …

The fundamental equations for Form II of Mindlin's second strain gradient elasticity theory for
isotropic materials are first derived. A corresponding simplified formulation is then proposed …

We formulate a discrete Lagrangian model for a set of interacting grains, which is purely
elastic. The considered degrees of freedom for each grain include placement of barycenter …

This article is devoted to isogeometric analysis of higher-order strain gradient elasticity by
user element implementations within a commercial finite element software Abaqus. The sixth …

This study focuses on the microarchitecture-dependent nonlinear bending behavior of
cellular plates with equitriangularly prismatic microarchitectures by adopting a dimensionally …

This article investigates the theoretical and numerical analysis as well as applications of the
three-dimensional theory of first strain gradient elasticity. The corresponding continuous and …

The nonlocal operator method (NOM) is initially proposed as a particle-based method, which
has difficulties in imposing accurately the boundary conditions of various orders. In this …

The main objective of this paper is to develop a theoretically and numerically reliable and
efficient methodology based on combining a finite element method and a strain gradient …

The classical continuum mechanics faces difficulties in solving problems involving highly
inhomogeneous deformations. The proposed theory investigates the impact of higher-order …