igUEL-SGE-solid: Abaqus user element (UEL) implementation for isogeometric analysis of strain-gradient-elastic solids

Generalized continuum theories such as strain gradient elasticity extend the classical single-scale continuum theories towards multi-scale physics. The present article presents an implementation of a user element for conforming isogeometric finite element analysis within the commercial finite element software Abaqus for analysing two- and three-dimensional solids within strain gradient elasticity. The implementation includes pre-processing, solution and post-processing modules for NURBS-based geometries, formation of element stiffness matrices and force vectors as well as result visualization, respectively. The overall software architecture and the content of the subroutines and input and output files of each module are described in detail. Example problems illustrate the use of the three modules: a rectangular strip in shear (2D); a square prism under body forces (3D); an annular prism in bending (3D).