A novel efficient mixed formulation for strain-gradient models.

Papanicolopulos, Stefanos-Aldo; Gulib, Fahad; Marinelli, Aikaterini

Abstract

Various finite elements based on mixed formulations have been proposed for the solution of boundary value problems involving strain-gradient models. The relevant literature, however, does not provide details on some important theoretical aspects of these elements. In this work we first present the existing elements within a novel, single mathematical framework, identifying some theoretical issues common to all of them that affect their robustness and numerical efficiency. We then proceed to develop a new family of mixed elements that addresses these issues, while being simpler and computationally cheaper. The behaviour of the new elements is further demonstrated through a numerical example.

Citation

Papanicolopulos, S.-A., Gulib, F., & Marinelli, A. (2019). A novel efficient mixed formulation for strain-gradient models. International Journal for Numerical Methods in Engineering, 117(8), 926-937. https://doi.org/10.1002/nme.5985

• Journal Article Type: Article
• Acceptance Date: Oct 29, 2018
• Online Publication Date: Nov 6, 2018
• Publication Date: Feb 24, 2019
• Deposit Date: Nov 1, 2018
• Publicly Available Date: Nov 6, 2018
• Journal: International Journal for Numerical Methods in Engineering
• Print ISSN: 0029-5981
• Electronic ISSN: 1097-0207
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 117
• Issue: 8
• Pages: 926-937
• DOI: https://doi.org/10.1002/nme.5985
• Keywords: Strain-gradient models, Finite element method, mixed formulation, penalty formulation,
• Public URL: http://researchrepository.napier.ac.uk/Output/1331660
• Contract Date: Nov 1, 2018