Sensitivity analysis based multi-scale methods of coupled path-dependent problems
Zupan, Nina (Author), Korelc, Jože (Author)

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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.

Keywords:dvo-nivojsko sledenje poti, metode na več skalah, občuljivostna analiza, mreža-v-elementu, FE2, two-level path-following, multi-scale methods, sensitivity analysis, mesh-in-element, FE2
Work type:Scientific work (r2)
Tipology:1.01 - Original Scientific Article
Organization:FGG - Faculty of Civil and Geodetic Engineering
Number of pages:str. 229-248
Numbering:Letn. 65, št. jan.
ISSN on article:0178-7675
DOI:10.1007/s00466-019-01762-8 Link is opened in a new window
COBISS.SI-ID:8898145 Link is opened in a new window
License:CC BY-NC-ND 4.0
This work is available under this license: Creative Commons Attribution Non-Commercial No Derivatives 4.0 International
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Title:Computational mechanics
Shortened title:Comput. mech.
COBISS.SI-ID:6668037 This link opens in a new window

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