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Computational homogenization for multi scale finite element simulation. / Arturo Jose Carneiro Molina

Swansea University Author: Arturo Jose Carneiro Molina

Abstract

This work presents a general formulation of small and large strain multiscale solid constitutive models based on the volume averaging of the microscopic strain (deformation gradient under large strain) and stress fields over a locally attached microstructure Representative Volume Element (RVE). Both...

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Published: 2007
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42431
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spelling 2018-08-02T16:24:29.2285866 v2 42431 2018-08-02 Computational homogenization for multi scale finite element simulation. b8f5e6b427d5fb85a7b01f2b2e0031c6 NULL Arturo Jose Carneiro Molina Arturo Jose Carneiro Molina true true 2018-08-02 This work presents a general formulation of small and large strain multiscale solid constitutive models based on the volume averaging of the microscopic strain (deformation gradient under large strain) and stress fields over a locally attached microstructure Representative Volume Element (RVE). Both elasto-plastic and hyperelastic behaviour are considered in the modelling of the RVE. A multiscale first-order computational homogenization method for modelling nonlinear deformation processes of evolving multi-phase materials is developed based on the Finite Element discretisation of both macro- and micro-structure. The approach consist of suitably imposing the macroscopic strain on the RVE and then computing the macroscopic stress as the volume average of the microscopic stress field obtained by solving numerically the local (initial) boundary value problem. In this context, the effective (homogenized) tangent modulus is obtained as a function of microstructure stiffness matrix which, in turn, depends upon the material properties and geometrical distribution of the micro-constituents in the RVE. The multiscale material presented here is restricted to two-dimensional problems, however we remark that the extension to three dimensions is trivial. The effectiveness of the proposed strategies is is demonstrated by means of numerical examples. E-Thesis Computational physics. 31 12 2007 2007-12-31 COLLEGE NANME Engineering COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:29.2285866 2018-08-02T16:24:29.2285866 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Arturo Jose Carneiro Molina NULL 1 0042431-02082018162453.pdf 10798139.pdf 2018-08-02T16:24:53.8770000 Output 10775123 application/pdf E-Thesis true 2018-08-02T16:24:53.8770000 false
title Computational homogenization for multi scale finite element simulation.
spellingShingle Computational homogenization for multi scale finite element simulation.
Arturo Jose Carneiro Molina
title_short Computational homogenization for multi scale finite element simulation.
title_full Computational homogenization for multi scale finite element simulation.
title_fullStr Computational homogenization for multi scale finite element simulation.
title_full_unstemmed Computational homogenization for multi scale finite element simulation.
title_sort Computational homogenization for multi scale finite element simulation.
author_id_str_mv b8f5e6b427d5fb85a7b01f2b2e0031c6
author_id_fullname_str_mv b8f5e6b427d5fb85a7b01f2b2e0031c6_***_Arturo Jose Carneiro Molina
author Arturo Jose Carneiro Molina
author2 Arturo Jose Carneiro Molina
format E-Thesis
publishDate 2007
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description This work presents a general formulation of small and large strain multiscale solid constitutive models based on the volume averaging of the microscopic strain (deformation gradient under large strain) and stress fields over a locally attached microstructure Representative Volume Element (RVE). Both elasto-plastic and hyperelastic behaviour are considered in the modelling of the RVE. A multiscale first-order computational homogenization method for modelling nonlinear deformation processes of evolving multi-phase materials is developed based on the Finite Element discretisation of both macro- and micro-structure. The approach consist of suitably imposing the macroscopic strain on the RVE and then computing the macroscopic stress as the volume average of the microscopic stress field obtained by solving numerically the local (initial) boundary value problem. In this context, the effective (homogenized) tangent modulus is obtained as a function of microstructure stiffness matrix which, in turn, depends upon the material properties and geometrical distribution of the micro-constituents in the RVE. The multiscale material presented here is restricted to two-dimensional problems, however we remark that the extension to three dimensions is trivial. The effectiveness of the proposed strategies is is demonstrated by means of numerical examples.
published_date 2007-12-31T03:52:57Z
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score 11.013015

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