Convergence analysis of Laplacian-based gradient elasticity in an isogeometric framework

Kolo, I. , Askes, H. and de Borst, R. (2017) Convergence analysis of Laplacian-based gradient elasticity in an isogeometric framework. Finite Elements in Analysis and Design, 135, pp. 56-67. (doi: 10.1016/j.finel.2017.07.006)

Abstract

A convergence study is presented for a form of gradient elasticity where the enrichment is through the Laplacian of the strain, so that a fourth-order partial differential equation results. Isogeometric finite element analysis is used to accommodate the higher continuity required by the inclusion of strain gradients. A convergence analysis is carried out for the original system of a fourth-order partial differential equation. Both global refinement, using NURBS, and local refinement, using T-splines, have been applied. Theoretical convergence rates are recovered, except for a polynomial order of two, when the convergence rate is suboptimal, a result which also has been found for the (fourth-order) Cahn-Hilliard equation. The convergence analyses have been repeated for the case that an operator split is applied so that a set of two (one-way) coupled partial differential equations results. Differences occur with the results obtained for the original fourth-order equation, which is caused by the boundary conditions, which is the first time this effect has been substantiated.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kolo, Dr Isa and De Borst, Professor Rene
• Authors: Kolo, I., Askes, H., and de Borst, R.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment; College of Science and Engineering > School of Engineering > Systems Power and Energy
• Journal Name: Finite Elements in Analysis and Design
• Publisher: Elsevier
• ISSN: 0168-874X
• ISSN (Online): 1872-6925
• Published Online: 24 July 2017