The purpose of this question is to determine the potential mechanical contribution of fibre-reinforced matrix in a tissue engineered structure for intervertebral disc repair. The base matrix is a hydrogel made of polycaprolactone dissolved in 2-hydroxyethylmethacrylate (known as a PHEMA hydrogel). The PHEMA hydrogel has desirable properties including high permeability to small molecules (e.g., tissue metabolites and waste) and hydrophilicity (attraction of water and ability to bind water) but its mechanical properties are not so good for physiological implantation. The elastic modulus of the PHEMA hydrogel is approximately EPHEMA = 9 MPa, and the maximal stress (failure stress) is OPHEMA = 2.4 MPa. The problem is that the failure stress of natural lumbar intervertebral disc tissue is about 22 MPa, and so the natural failure stress of the PHEMA hydrogel is too low. To improve the strength of the structure, polyethylenetherephtalate (PET) fibres can be added to the hydrogel. The modulus of elasticity of the PET fibres is EPET = 43 MPa. Based on this information, calculate what the effect is on relative load distribution between the components if you add PET fibres to the matrix to either 15% or 40% volume fraction (i.e, What percentage of the applied force is carried by hydrogel and what percentage is carried by PET fibres at each of these two percentages?) 1) Assume that the distribution of fibres is uniform throughout. That helps with the next two points. 2) Assume that the structure has a “unit length" and so relative volume fraction can be assumed to be an "area fraction" (i.e., a percentage of the cross-sectional area of the loaded structure). 3) And so, based on the first two points, assume that the addition of the fibres (by volume fraction) has a proportional contribution to the load carrying capacity (in other words, it obeys the mathematical relationship for fibre-reinforced matrices
The purpose of this question is to determine the potential mechanical contribution of fibre-reinforced matrix in a tissue engineered structure for intervertebral disc repair. The base matrix is a hydrogel made of polycaprolactone dissolved in 2-hydroxyethylmethacrylate (known as a PHEMA hydrogel). The PHEMA hydrogel has desirable properties including high permeability to small molecules (e.g., tissue metabolites and waste) and hydrophilicity (attraction of water and ability to bind water) but its mechanical properties are not so good for physiological implantation. The elastic modulus of the PHEMA hydrogel is approximately EPHEMA = 9 MPa, and the maximal stress (failure stress) is OPHEMA = 2.4 MPa. The problem is that the failure stress of natural lumbar intervertebral disc tissue is about 22 MPa, and so the natural failure stress of the PHEMA hydrogel is too low. To improve the strength of the structure, polyethylenetherephtalate (PET) fibres can be added to the hydrogel. The modulus of elasticity of the PET fibres is EPET = 43 MPa. Based on this information, calculate what the effect is on relative load distribution between the components if you add PET fibres to the matrix to either 15% or 40% volume fraction (i.e, What percentage of the applied force is carried by hydrogel and what percentage is carried by PET fibres at each of these two percentages?) 1) Assume that the distribution of fibres is uniform throughout. That helps with the next two points. 2) Assume that the structure has a “unit length" and so relative volume fraction can be assumed to be an "area fraction" (i.e., a percentage of the cross-sectional area of the loaded structure). 3) And so, based on the first two points, assume that the addition of the fibres (by volume fraction) has a proportional contribution to the load carrying capacity (in other words, it obeys the mathematical relationship for fibre-reinforced matrices
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Transcribed Image Text:The purpose of this question is to determine the potential mechanical contribution of fibre-reinforced matrix in a tissue
engineered structure for intervertebral disc repair. The base matrix is a hydrogel made of polycaprolactone dissolved in
2-hydroxyethylmethacrylate (known as a PHEMA hydrogel). The PHEMA hydrogel has desirable properties including
high permeability to small molecules (e.g., tissue metabolites and waste) and hydrophilicity (attraction of water and
ability to bind water) but its mechanical properties are not so good for physiological implantation. The elastic modulus
of the PHEMA hydrogel is approximately EPHEMA = 9 MPa, and the maximal stress (failure stress) is OPHEMA = 2.4 MPa.
The problem is that the failure stress of natural lumbar intervertebral disc tissue is about 22 MPa, and so the natural
failure stress of the PHEMA hydrogel is too low. To improve the strength of the structure, polyethylenetherephtalate
(PET) fibres can be added to the hydrogel. The modulus of elasticity of the PET fibres is EPET = 43 MPa.
Based on this information, calculate what the effect is on relative load distribution between the components if you
add PET fibres to the matrix to either 15% or 40% volume fraction (i.e, What percentage of the applied force is
carried by hydrogel and what percentage is carried by PET fibres at each of these two percentages?)
Transcribed Image Text:1) Assume that the distribution of fibres is uniform throughout. That helps with the next two points.
2) Assume that the structure has a “unit length" and so relative volume fraction can be assumed to be an "area
fraction" (i.e., a percentage of the cross-sectional area of the loaded structure).
3) And so, based on the first two points, assume that the addition of the fibres (by volume fraction) has a
proportional contribution to the load carrying capacity (in other words, it obeys the mathematical relationship
for fibre-reinforced matrices
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