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Simulation tools for biomechanical applications with PGD-based reduced order models

Xi Zou Orcid Logo

Swansea University Author: Xi Zou Orcid Logo

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Numerical simulation tools are generally used in all modern engineering fields, especially those having difficulties in performing large number of practical experiments, such as biomechanics. Among the computational methods, Finite Element (FE) is an essential tool. Nowadays, the fast-growing comput...

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Published: Universitat Politècnica de Catalunya 2018
Online Access: https://www.tdx.cat/handle/10803/481988#page=1
URI: https://cronfa.swan.ac.uk/Record/cronfa65265
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Nowadays, the fast-growing computational techniques, from the upgrading hardware to the emerging of novel algorithm, have already enabled extensive applications in biomechanics. For applications that require fast response and/or multiple queries, Reduced Order Modelling (ROM) methods have been developed based on existing methods such as FE, and have eventually enabled real-time numerical simulation for a large variety of engineering problems. In this thesis, several novel computational techniques are developed to explore the capability of Proper Generalised Decomposition (PGD), which is an important approach of ROM. To assess the usability of the PGD-based ROM for biomechanical applications, a real human femur bone is chosen to study its mechanical behaviour as an example. Standard image-based modelling procedure in biomechanics is performed to create an FE model which is then validated with in vitro experimental results. As a basis of this work, the medical image processing has to be performed, in order to generate an available FE model. This model is validated according to data collected from a previously performed \textit{in vitro} experimental test. The full procedure of image-based model generation and the validation of generated model is described in Chapter 2. As a major objective of this thesis, a non-intrusive scheme for the PGD framework is developed in Chapter 3. It is implemented using in-house developed Matlab (Mathworks, USA) code to conduct the PGD work flow, and calling Abaqus as an external solver for devised fictitious mechanical problems. The transformation of data from computed tomography (CT) image set to FE model including inhomogeneous material properties is subjected to some physical constraints, and when applying the load, there are also geometric constraints limiting the locations where load could be applied. These constraints will lead to a constrained parameter space, which possibly has difficulty to be separated in a Cartesian fashion. Therefore, a novel strategy to separate the parameters in a collective manner is proposed in Chapter 4. Chapter 5 details a comprehensive application in biomechanics, the methodologies proposed in Chapter 3 and 4 are applied on the practical model generated in Chapter 2. As a typical application of the PGD vademecum, a material property identification problem is discussed. Further PGD vademecum is generated using the identified material properties with variable loading locations, and with this vademecum, real-time mechanical response of the femur is available. In addition, for the purpose of extending the methodologies to orthotropic materials, which is commonly used in biomechanics, in Chapter 6 another linear elastic model is investigated with the non-intrusive PGD scheme. Nowadays, isogeometric analysis (IGA) is a very popular tool in computational mechanics. It is appealing to take advantage of non-uniform rational B-splines (NURBS) to discretise the model. For PGD, using B-splines for the discretisation of the parameter space could improve the quality of vademecum, especially for problems involving sensitivities with respect to the parameters during the online computations. It is important and necessary to extend the PGD framework to nonlinear solid mechanics, because most biological soft tissues have been observed nonlinear mechanical behaviours. Consequently, in Chapter 7 we have developed a PGD framework for the St.Venant-Kirchhoff constitutive model using the Picard linearisation which is consistent with the fixed-point iteration algorithm commonly used in PGD. In Chapter 8, conclusive remarks are addressed as well as forecasts of possible future works.</abstract><type>Thesis</type><journal/><volume/><journalNumber/><paginationStart/><paginationEnd/><publisher/><placeOfPublication>Universitat Politècnica de Catalunya</placeOfPublication><isbnPrint/><isbnElectronic/><issnPrint/><issnElectronic/><keywords/><publishedDay>12</publishedDay><publishedMonth>3</publishedMonth><publishedYear>2018</publishedYear><publishedDate>2018-03-12</publishedDate><doi/><url>https://www.tdx.cat/handle/10803/481988#page=1</url><notes>https://www.tdx.cat/handle/10803/481988#page=1</notes><college>COLLEGE NANME</college><department>Aerospace Engineering</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>AERO</DepartmentCode><institution>Swansea University</institution><apcterm/><funders/><projectreference/><lastEdited>2024-04-11T19:52:06.3116123</lastEdited><Created>2023-12-11T10:21:20.9489177</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering</level></path><authors><author><firstname>Xi</firstname><surname>Zou</surname><orcid>0000-0001-7436-7903</orcid><order>1</order></author></authors><documents/><OutputDurs/></rfc1807>
spelling v2 65265 2023-12-11 Simulation tools for biomechanical applications with PGD-based reduced order models a9f66a1e56009848af57c0d174d08ffe 0000-0001-7436-7903 Xi Zou Xi Zou true false 2023-12-11 AERO Numerical simulation tools are generally used in all modern engineering fields, especially those having difficulties in performing large number of practical experiments, such as biomechanics. Among the computational methods, Finite Element (FE) is an essential tool. Nowadays, the fast-growing computational techniques, from the upgrading hardware to the emerging of novel algorithm, have already enabled extensive applications in biomechanics. For applications that require fast response and/or multiple queries, Reduced Order Modelling (ROM) methods have been developed based on existing methods such as FE, and have eventually enabled real-time numerical simulation for a large variety of engineering problems. In this thesis, several novel computational techniques are developed to explore the capability of Proper Generalised Decomposition (PGD), which is an important approach of ROM. To assess the usability of the PGD-based ROM for biomechanical applications, a real human femur bone is chosen to study its mechanical behaviour as an example. Standard image-based modelling procedure in biomechanics is performed to create an FE model which is then validated with in vitro experimental results. As a basis of this work, the medical image processing has to be performed, in order to generate an available FE model. This model is validated according to data collected from a previously performed \textit{in vitro} experimental test. The full procedure of image-based model generation and the validation of generated model is described in Chapter 2. As a major objective of this thesis, a non-intrusive scheme for the PGD framework is developed in Chapter 3. It is implemented using in-house developed Matlab (Mathworks, USA) code to conduct the PGD work flow, and calling Abaqus as an external solver for devised fictitious mechanical problems. The transformation of data from computed tomography (CT) image set to FE model including inhomogeneous material properties is subjected to some physical constraints, and when applying the load, there are also geometric constraints limiting the locations where load could be applied. These constraints will lead to a constrained parameter space, which possibly has difficulty to be separated in a Cartesian fashion. Therefore, a novel strategy to separate the parameters in a collective manner is proposed in Chapter 4. Chapter 5 details a comprehensive application in biomechanics, the methodologies proposed in Chapter 3 and 4 are applied on the practical model generated in Chapter 2. As a typical application of the PGD vademecum, a material property identification problem is discussed. Further PGD vademecum is generated using the identified material properties with variable loading locations, and with this vademecum, real-time mechanical response of the femur is available. In addition, for the purpose of extending the methodologies to orthotropic materials, which is commonly used in biomechanics, in Chapter 6 another linear elastic model is investigated with the non-intrusive PGD scheme. Nowadays, isogeometric analysis (IGA) is a very popular tool in computational mechanics. It is appealing to take advantage of non-uniform rational B-splines (NURBS) to discretise the model. For PGD, using B-splines for the discretisation of the parameter space could improve the quality of vademecum, especially for problems involving sensitivities with respect to the parameters during the online computations. It is important and necessary to extend the PGD framework to nonlinear solid mechanics, because most biological soft tissues have been observed nonlinear mechanical behaviours. Consequently, in Chapter 7 we have developed a PGD framework for the St.Venant-Kirchhoff constitutive model using the Picard linearisation which is consistent with the fixed-point iteration algorithm commonly used in PGD. In Chapter 8, conclusive remarks are addressed as well as forecasts of possible future works. Thesis Universitat Politècnica de Catalunya 12 3 2018 2018-03-12 https://www.tdx.cat/handle/10803/481988#page=1 https://www.tdx.cat/handle/10803/481988#page=1 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2024-04-11T19:52:06.3116123 2023-12-11T10:21:20.9489177 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Xi Zou 0000-0001-7436-7903 1
title Simulation tools for biomechanical applications with PGD-based reduced order models
spellingShingle Simulation tools for biomechanical applications with PGD-based reduced order models
Xi Zou
title_short Simulation tools for biomechanical applications with PGD-based reduced order models
title_full Simulation tools for biomechanical applications with PGD-based reduced order models
title_fullStr Simulation tools for biomechanical applications with PGD-based reduced order models
title_full_unstemmed Simulation tools for biomechanical applications with PGD-based reduced order models
title_sort Simulation tools for biomechanical applications with PGD-based reduced order models
author_id_str_mv a9f66a1e56009848af57c0d174d08ffe
author_id_fullname_str_mv a9f66a1e56009848af57c0d174d08ffe_***_Xi Zou
author Xi Zou
author2 Xi Zou
format Staff Thesis
publishDate 2018
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 Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
url https://www.tdx.cat/handle/10803/481988#page=1
document_store_str 0
active_str 0
description Numerical simulation tools are generally used in all modern engineering fields, especially those having difficulties in performing large number of practical experiments, such as biomechanics. Among the computational methods, Finite Element (FE) is an essential tool. Nowadays, the fast-growing computational techniques, from the upgrading hardware to the emerging of novel algorithm, have already enabled extensive applications in biomechanics. For applications that require fast response and/or multiple queries, Reduced Order Modelling (ROM) methods have been developed based on existing methods such as FE, and have eventually enabled real-time numerical simulation for a large variety of engineering problems. In this thesis, several novel computational techniques are developed to explore the capability of Proper Generalised Decomposition (PGD), which is an important approach of ROM. To assess the usability of the PGD-based ROM for biomechanical applications, a real human femur bone is chosen to study its mechanical behaviour as an example. Standard image-based modelling procedure in biomechanics is performed to create an FE model which is then validated with in vitro experimental results. As a basis of this work, the medical image processing has to be performed, in order to generate an available FE model. This model is validated according to data collected from a previously performed \textit{in vitro} experimental test. The full procedure of image-based model generation and the validation of generated model is described in Chapter 2. As a major objective of this thesis, a non-intrusive scheme for the PGD framework is developed in Chapter 3. It is implemented using in-house developed Matlab (Mathworks, USA) code to conduct the PGD work flow, and calling Abaqus as an external solver for devised fictitious mechanical problems. The transformation of data from computed tomography (CT) image set to FE model including inhomogeneous material properties is subjected to some physical constraints, and when applying the load, there are also geometric constraints limiting the locations where load could be applied. These constraints will lead to a constrained parameter space, which possibly has difficulty to be separated in a Cartesian fashion. Therefore, a novel strategy to separate the parameters in a collective manner is proposed in Chapter 4. Chapter 5 details a comprehensive application in biomechanics, the methodologies proposed in Chapter 3 and 4 are applied on the practical model generated in Chapter 2. As a typical application of the PGD vademecum, a material property identification problem is discussed. Further PGD vademecum is generated using the identified material properties with variable loading locations, and with this vademecum, real-time mechanical response of the femur is available. In addition, for the purpose of extending the methodologies to orthotropic materials, which is commonly used in biomechanics, in Chapter 6 another linear elastic model is investigated with the non-intrusive PGD scheme. Nowadays, isogeometric analysis (IGA) is a very popular tool in computational mechanics. It is appealing to take advantage of non-uniform rational B-splines (NURBS) to discretise the model. For PGD, using B-splines for the discretisation of the parameter space could improve the quality of vademecum, especially for problems involving sensitivities with respect to the parameters during the online computations. It is important and necessary to extend the PGD framework to nonlinear solid mechanics, because most biological soft tissues have been observed nonlinear mechanical behaviours. Consequently, in Chapter 7 we have developed a PGD framework for the St.Venant-Kirchhoff constitutive model using the Picard linearisation which is consistent with the fixed-point iteration algorithm commonly used in PGD. In Chapter 8, conclusive remarks are addressed as well as forecasts of possible future works.
published_date 2018-03-12T19:52:01Z
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score 11.014537

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