Pan, Chunlin
(2017)
Effects of Shape and Material Mismatch on 2D Finite Domains containing Inclusions.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
To develop a sustainable built environment, a realistic prediction of critical structures residing on a microstructure-based approximation of the material behavior is of fundamental importance. Characterization of the elastic fields inside representative volume elements (RVEs) is the key to accomplish this approximation. In this research, an investigation is carried out to seek for the solutions of 2D bounded RVEs containing homogeneous and inhomogeneous inclusions. Based on the fundamental works by Muskhelishvilli (1953) on Riemann Hilbert Problem, the complex potential formulation is employed to analytically investigate the disturbance inside the finite domain induced by the material mismatch or eigenstrains. According to Sokhotski-Plemelj Theorem, the potentials in inclusions and the matrix are constructed in the form of Laurent series at the center of each corresponding domain. Then with the help of the independence of the linear group of exponential terms, the interfacial condition of continuity and equilibrium between the inclusions and the matrix, as well as the exterior Dirichlet boundary conditions, can be explicitly expressed as algebraic equations, which lead to the identification of the coefficients in Laurent series. The shape effect of the bounded matrix is also captured by coupling this approach with conformal mapping strategy, while to study the complicatedly shaped inclusions, the singly connected curves of interfaces are replaced with piecewise straight lines. The analytical solution obtained can provide a deep understanding of the RVEs on capturing the local elastic fields at the micro-scale as well as on estimating the overall effective elastic moduli at the macro-scale. The obtained solutions are documented in this dissertation and can be applied directly in a wide variety of engineering applications, which include the homogeneous inclusions with arbitrary shapes and inhomogeneous inclusions with multi-layers structure.
Share
| Citation/Export: |
|
| Social Networking: |
|
Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| Date: |
1 February 2017 |
| Date Type: |
Publication |
| Defense Date: |
1 November 2016 |
| Approval Date: |
1 February 2017 |
| Submission Date: |
30 November 2016 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
175 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Swanson School of Engineering > Civil and Environmental Engineering |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Inclusion Problem, Finite Domains, Eigenstrain, Representative Volume Elements, Complex Potential Method, Conformal Mapping. |
| Date Deposited: |
01 Feb 2017 19:42 |
| Last Modified: |
02 Feb 2017 06:15 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/30360 |
Metrics
Monthly Views for the past 3 years
Plum Analytics
Actions (login required)
 |
View Item |
![[feed]](/images/feed-icon-32x32.png){kind=icon}