74 Mechanics of deformable solids -- 74C Plastic materials, materials of stress-rate and internal-variable type 74C05 Small-strain, rate-independent theories
74 Mechanics of deformable solids -- 74S Numerical methods 74S05 Finite element methods
Summary: ``This paper presents finite element implementations for the solution of gradient elasticity problems using the FEniCS project. The FEniCS Project provides a novel tool for the automated solution of partial differential equations by the finite element method. In particular, it offers a significant flexibility with regards to modelling and numerical discretization choices. The weak form of the gradient elasticity problem is derived from the Principal of Virtual Work. An equivalent mixed-type finite element formulation for the strain gradient elasticity problem is implemented in order to avoid the use of $C^1$ continuous elements. The complete methodology and source codes (python scripts) are provided. Numerical results are presented and compared with well-known benchmark examples, demonstrating the applicability of FEniCS for such applications.''