Isogeometric static analysis of gradient-elastic plane strain/stress problems

In the present contribution, isogeometric methods are used to analyze the statics of the plane strain and plane stress problems based on the theory of strain gradient elasticity. The adopted strain gradient elasticity models, in particular, include only one length scale parameter enriching the classical strain energy expression and resulting in fourth order partial differential equations instead of the corresponding second order ones based on the classical elasticity. The problems are discretized by an isogeometric NURBS based C1C1 continuous Galerkin method which is implemented as a user subroutine into a commercial software Abaqus. Computational results for benchmark problems, a square plate in tension and a Lamé problem, demonstrate the applicability of the method and verify the implementation.