Authors: Kaiser, Tobias
Forest, Samuel
Menzel, Andreas
Title: A finite element implementation of the stress gradient theory
Language (ISO): en
Abstract: In this contribution, a finite element implementation of the stress gradient theory is proposed. The implementation relies on a reformulation of the governing set of partial differential equations in terms of one primary tensor-valued field variable of third order, the so-called generalised displacement field. Whereas the volumetric part of the generalised displacement field is closely related to the classic displacement field, the deviatoric part can be interpreted in terms of micro-displacements. The associated weak formulation moreover stipulates boundary conditions in terms of the normal projection of the generalised displacement field or of the (complete) stress tensor. A detailed study of representative boundary value problems of stress gradient elasticity shows the applicability of the proposed formulation. In particular, the finite element implementation is validated based on the analytical solutions for a cylindrical bar under tension and torsion derived by means of Bessel functions. In both tension and torsion cases, a smaller is softer size effect is evidenced in striking contrast to the corresponding strain gradient elasticity solutions.
Subject Headings: Generalised continuum
Stress gradient theory
Stress gradient elasticity
Strain gradient elasticity
Finite elements
Analytical solutions
Subject Headings (RSWK): Kontinuumsmechanik
Analytische Lösung
Mindlin-Reissner plate theory
Issue Date: 2021-03-02
Rights link:
Appears in Collections:Institut für Mechanik

Files in This Item:
File Description SizeFormat 
Kaiser2021_Article_AFiniteElementImplementationOf.pdf3.07 MBAdobe PDFView/Open

This item is protected by original copyright

This item is licensed under a Creative Commons License Creative Commons