Sensitivity analysis based multi-scale methods of coupled path-dependent problems

Zupan, Nina (author), Korelc, Jože (author)

In the paper, a generalized essential boundary condition sensitivity analysis based implementation of FE2 and mesh-inelement (MIEL) multi-scale methods is derived as an alternative to standard implementations of multi-scale analysis, where the calculation of Schur complement of the microscopic tangent matrix is needed for bridging the scales. The paper presents a unified approach to the development of an arbitrary MIEL or FE2 computational scheme for an arbitrary path-dependent material model. Implementation is based on efficient first and second order analytical sensitivity analysis, for which automaticdifferentiation-based formulation of essential boundary condition sensitivity analysis is derived. A fully consistently linearized two-level path-following algorithm is introduced as a solution algorithm for the multi-scale modeling. Sensitivity analysis allows each macro step to be followed by an arbitrary number of micro substeps while retaining quadratic convergence of the overall solution algorithm.

• Language: English
• Keywords: two-level path-following, multi-scale methods, sensitivity analysis, mesh-in-element, FE$^2$
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2020
• Number of pages: Str. 229-248
• Numbering: Vol. 65, iss. 1
• PID: 20.500.12556/RUL-114128
• UDC: 531/533
• ISSN on article: 0178-7675
• DOI: 10.1007/s00466-019-01762-8
• COBISS.SI-ID: 8898145
• Publication date in RUL: 18.02.2020

Record is a part of a journal

• Title: Computational mechanics
• Shortened title: Comput. mech.
• Publisher: Springer
• ISSN: 0178-7675
• COBISS.SI-ID: 6668037

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.
• Licensing start date: 01.01.2020

Secondary language

• Language: Slovenian
• Keywords: dvo-nivojsko sledenje poti, metode na več skalah, občuljivostna analiza, mreža-v-elementu, FE$^2$

Projects

• Funder: ARRS - Slovenian Research Agency
• Funding programme: Young researchers
• Project number: 630-34/2015-7