The objectives of this work are to discuss multiscale models that are used to characterize the constitutive relations of the granular composite materials with dual functions. This is accomplished by the use of ab initio methods to obtain the constitutive relations of the structural energetic materials without conducting tests. First, it is necessary to study the quantum many body problem to quantitatively determine the internal energy of the material when subjected to different strain conditions. It is impossible to obtain an exact solution to the quantum many body problem that is modeled by the Schrödinger's equations with the current technology. It is possible to solve these equations approximately by the density functional theory which yields only energies at absolute 0ºK. Thus it becomes necessary to add both the lattice thermal contributions and electron thermal contribution. Then, resulting energy is used to bridge to the continuum level and obtain the constitutive equations. This is the procedure that is used in this work.
The issues of the constitutive equations form the focus of this thesis. More specifically, the scope of the thesis is further restricted to analyze the constitutive equations of specific mixtures of nickel, aluminum with PTFE or Teflon as the binder. It is to be noted that the equations of state forms only a part of the complete constitutive relationships. This thesis presents solutions to the following problems:
(1) Determination of the thermodynamically complete equation of state of the binder and the energetic material PTFE or Teflon, from ab initio methods based on the density functional theory.
(2) Determination of the equations of state of the granular composite or the mixture of nickel, aluminum and PTFE from ab initio methods.
(3) Determination of the complete constitutive equation of aluminum, from ab initio methods, under conditions of finite deformations, with principle of objectivity, material symmetry conditions and polyconvexity of the strain energy.
All results are compared to test results whenever they are available.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/29696 |
| Date | 14 May 2009 |
| Creators | Wu, Zhibo |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Detected Language | English |
| Type | Dissertation |
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