A finite element implementation of the stress gradient theory

Abstract In this contribution, a finite element implementation of the stress gradient theory is proposed. The relies on reformulation governing set partial differential equations in terms one primary tensor-valued field variable third order, so-called generalised displacement field. Whereas volumetric part closely related to classic field, deviatoric can be interpreted micro-displacements. associated weak formulation moreover stipulates boundary conditions normal projection or (complete) tensor. A detailed study representative value problems elasticity shows applicability proposed formulation. particular, validated based analytical solutions for cylindrical bar under tension and torsion derived by means Bessel functions. both cases, smaller softer size effect evidenced striking contrast corresponding strain solutions.