Meshfree Modelling of Hyperelastic Mechanics
type: CreativeWork
description: Large deformation mechanics faces numerous challenges when simulated using mesh-based methods, notably the finite element method. Firstly, the computational modeler is required to fit a mesh to the body of interest, which is a tedious and time-consuming process. Secondly, these meshes are typically simplex shapes and therefore can resist deformation artificially as their deformation increases, and numerical instability can occur as these simplexes/polygons invert for deformation beyond their resolution. Thirdly, these meshes can be resolved further into smaller pieces, a process called refinement, but the process of robust automatic refinement is still another challenge face by modelers. Therefore, in this thesis, we are motivated to use a meshfree method to simulate large deformations of hyperelastic mechanics without the dependency of a body mesh. The thesis then explores some of the challenges faced by meshfree methods currently and further developing and maturing its strengths of solving PDEs with only random nodal distributions. We found that these meshfree methods often depends on a background mesh for quadrature process, hence currently many meshfree methods are still not as “mesh-independent” as we wish them to be. Therefore we attempted to develop a truly meshfree method is in this thesis, where the quadrature is performed in overlapping support domains of a set of functions that form partition of unity of the body. We manage to improve on the Partition of Unity Quadrature scheme, where polynomial consistency can be restored for the first time in overlapping quadrature schemes, while still conserving energy according to the work conjugacy theory. The methods fall short that the quadrature accuracy must be increased with refinement of particle distributions, a common observation among truly meshfree methods. Another issue that meshfree methods faces is the ability to enforce incompressibility in solid mechanics. Hyperelasticity does not only undergo large de…
abstract: Large deformation mechanics faces numerous challenges when simulated using mesh-based methods, notably the finite element method. Firstly, the computational modeler is required to fit a mesh to the body of interest, which is a tedious and time-consuming process. Secondly, these meshes are typically simplex shapes and therefore can resist deformation artificially as their deformation increases, and numerical instability can occur as these simplexes/polygons invert for deformation beyond their resolution. Thirdly, these meshes can be resolved further into smaller pieces, a process called refinement, but the process of robust automatic refinement is still another challenge face by modelers. Therefore, in this thesis, we are motivated to use a meshfree method to simulate large deformations of hyperelastic mechanics without the dependency of a body mesh. The thesis then explores some of the challenges faced by meshfree methods currently and further developing and maturing its strengths of solving PDEs with only random nodal distributions. We found that these meshfree methods often depends on a background mesh for quadrature process, hence currently many meshfree methods are still not as “mesh-independent” as we wish them to be. Therefore we attempted to develop a truly meshfree method is in this thesis, where the quadrature is performed in overlapping support domains of a set of functions that form partition of unity of the body. We manage to improve on the Partition of Unity Quadrature scheme, where polynomial consistency can be restored for the first time in overlapping quadrature schemes, while still conserving energy according to the work conjugacy theory. The methods fall short that the quadrature accuracy must be increased with refinement of particle distributions, a common observation among truly meshfree methods. Another issue that meshfree methods faces is the ability to enforce incompressibility in solid mechanics. Hyperelasticity does not only undergo large de…
author: Goh, Chun Meng
license: https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
date published: 2020
date modified: 2026-07-24T01:02:59Z
provider: University of Auckland
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: ResearchSpace@Auckland

PropertyValue
property ID: Handle
value: https://hdl.handle.net/2292/53393