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

In the paper, a generalized essential boundary condition sensitivity analysis based implementation of FE 2 and mesh-in-element (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 tan...

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Bibliographic Details
Published in:Computational mechanics 2020, Vol.65 (1), p.229-248
Main Authors: Zupan, Nina, Korelc, Jože
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Boundary conditions
Classical and Continuum Physics
Computational Science and Engineering
Engineering
Finite element method
Methods
Multiscale analysis
Original Paper
Sensitivity analysis
Theoretical and Applied Mechanics
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Summary:In the paper, a generalized essential boundary condition sensitivity analysis based implementation of FE 2 and mesh-in-element (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 FE 2 computational scheme for an arbitrary path-dependent material model. Implementation is based on efficient first and second order analytical sensitivity analysis, for which automatic-differentiation-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.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-019-01762-8