An improved local radial basis function method for solving small-strain elasto-plasticity

Vuga, Gašper (author), Mavrič, Boštjan (author), Šarler, Božidar (author)

Strong-form meshless methods received much attention in recent years and are being extensively researched and applied to a wide range of problems in science and engineering. However, the solution of elasto-plastic problems has proven to be elusive because of often non-smooth constitutive relations between stress and strain. The novelty in tackling them is the introduction of virtual finite difference stencils to formulate a hybrid radial basis function generated finite difference (RBF-FD) method, which is used to solve small-strain von Mises elasto-plasticity for the first time by this original approach. The paper further contrasts the new method to two alternative legacy RBF-FD approaches, which fail when applied to this class of problems. The three approaches differ in the discretization of the divergence operator found in the balance equation that acts on the non-smooth stress field. Additionally, an innovative stabilization technique is employed to stabilize boundary conditions and is shown to be essential for any of the approaches to converge successfully. Approaches are assessed on elastic and elasto-plastic benchmarks where admissible ranges of newly introduced free parameters are studied regarding stability, accuracy, and convergence rate.

• Language: English
• Keywords: Von Mises elasto-plasticity, radial basis function, finite differences, polyharmonic splines, two dimensions, hybrid discretization, radial basis function generated finite differences
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2024
• Number of pages: 28 str.
• Numbering: Vol. 418, pt. A, art. 116501
• PID: 20.500.12556/RUL-151689
• UDC: 539.3
• ISSN on article: 0045-7825
• DOI: 10.1016/j.cma.2023.116501
• COBISS.SI-ID: 168587267
• Publication date in RUL: 16.10.2023

Record is a part of a journal

• Title: Computer methods in applied mechanics and engineering
• Shortened title: Comput. methods appl. mech. eng.
• Publisher: Elsevier
• ISSN: 0045-7825
• COBISS.SI-ID: 6695685

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: elasto-plastičnost, radialne bazne funkcije, končne diference, dvodimenzionalnost, hibridna diskretizacija