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The finite cell method for the computation of cellular materials
Citation Link: https://doi.org/10.15480/882.2526
Publikationstyp
Doctoral Thesis
Date Issued
2019
Sprache
English
Author(s)
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2019-03-25
TORE-DOI
TORE-URI
Open cell aluminum foams present an attractive class of materials that are applied in many
engineering disciplines ranging from automotive, naval and aerospace industry to biomedical
applications. In order to design engineering structures composed of foams, a detailed experimental
and numerical investigation of their mechanical properties is necessary. The structure
of metal foams consists of a complicated stochastic distribution of pores which requires an immense
labor effort to generate a suitable finite element discretization. The finite cell method
is a combination of the fictitious domain approach and high order finite elements. Due to the
fictitious domain approach the finite cell method has shown to drastically simplify the mesh
generation process. Motivated by this promising property we employ the finite cell method
and enhance it in order to investigate the mechanical behavior of aluminum foams.
The following topics are addressed in this thesis:
The starting point for any numerical investigation is the discretization of the geometry. A
realistic geometric model of metal foams can be provided using voxel models stemming from
computed tomography scans. Such models are of course not free from artifacts. In order
to achieve automatic mesh generation for voxel-based models, algorithms known from
computer graphics will be applied to remove these artifacts. In addition voxel models will
be modified numerically for example by the application of a thin coating to the metal foams.
The effect of the coating on the homogenized elastic properties will be examined using the
window method. In order to accelerate the homogenization procedure Aitken’s 2-method
will be applied in this context.
To study the buckling and the finite elastoplastic deformations of cell walls the finite cell
method will be extended by a hyperelastic based von Mises plasticity model which makes use
of the multiplicative split of the deformation gradient into its elastic and plastic contributions.
By employing this model different structural levels of the aluminum metal foams will be analyzed
under large deformations. A focus here is on the investigation of single pores that
serve to find the microscopic material properties of the aluminum by combining experiments
and simulations on pores. Finally computations of larger foam samples will be carried out
aiming to find a representative volume element and to verify the material parameters obtained
by single pore experiments and inverse computations.
Two different contact formulations based on the penalty method – one for sticking and one
for frictionless contact conditions – will be introduced and investigated by comparing their
results to the analytical solution derived by Hertz. The self-contact of metal foams will
be modeled using sticking contact formulation and finally applied to a single pore to show the
influence of self-contact on the load displacement curve.
engineering disciplines ranging from automotive, naval and aerospace industry to biomedical
applications. In order to design engineering structures composed of foams, a detailed experimental
and numerical investigation of their mechanical properties is necessary. The structure
of metal foams consists of a complicated stochastic distribution of pores which requires an immense
labor effort to generate a suitable finite element discretization. The finite cell method
is a combination of the fictitious domain approach and high order finite elements. Due to the
fictitious domain approach the finite cell method has shown to drastically simplify the mesh
generation process. Motivated by this promising property we employ the finite cell method
and enhance it in order to investigate the mechanical behavior of aluminum foams.
The following topics are addressed in this thesis:
The starting point for any numerical investigation is the discretization of the geometry. A
realistic geometric model of metal foams can be provided using voxel models stemming from
computed tomography scans. Such models are of course not free from artifacts. In order
to achieve automatic mesh generation for voxel-based models, algorithms known from
computer graphics will be applied to remove these artifacts. In addition voxel models will
be modified numerically for example by the application of a thin coating to the metal foams.
The effect of the coating on the homogenized elastic properties will be examined using the
window method. In order to accelerate the homogenization procedure Aitken’s 2-method
will be applied in this context.
To study the buckling and the finite elastoplastic deformations of cell walls the finite cell
method will be extended by a hyperelastic based von Mises plasticity model which makes use
of the multiplicative split of the deformation gradient into its elastic and plastic contributions.
By employing this model different structural levels of the aluminum metal foams will be analyzed
under large deformations. A focus here is on the investigation of single pores that
serve to find the microscopic material properties of the aluminum by combining experiments
and simulations on pores. Finally computations of larger foam samples will be carried out
aiming to find a representative volume element and to verify the material parameters obtained
by single pore experiments and inverse computations.
Two different contact formulations based on the penalty method – one for sticking and one
for frictionless contact conditions – will be introduced and investigated by comparing their
results to the analytical solution derived by Hertz. The self-contact of metal foams will
be modeled using sticking contact formulation and finally applied to a single pore to show the
influence of self-contact on the load displacement curve.
Subjects
Finite cell method
Metal foams
DDC Class
600: Technik
620: Ingenieurwissenschaften
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