HOMOGENEOUS CONSTITUTIVE EQUATIONS FOR MATERIALS WITH PERMANENT MEMORY
UTAH UNIV SALT LAKE CITY COLL OF ENGINEERING
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Nonlinear homogeneous constitutive equations are developed in this thesis for highly filled polymeric materials such as solid propellants. In the range of strains below vacuole dilatation these materials obey the homogeneity rule of linearity but do not obey the superposition rule. Such materials typically exhibit an irreversible stress softening called the Mullins Effect. The development in this dissertation stems from attempting to mathematically describe the failing microstructure of these composite materials in terms of a linear cumulative damage model. It is demonstrated that pth order Lebesgue norms of the strain history can be used to describe the state of damage in these materials and can also be used in the constitutive equation to characterize their time dependent mechanical response to strain disturbances. Stress analysis procedures for materials having nonlinear homogeneous constitutive equations are developed for two and three dimensional proportional boundary value problems. A series of correspondence principles are derived wherein half of the solution, either the stresses or the strains, can be obtained by solving an equivalent linear elastic problem. The remaining half of the solution can be obtained by substituting the linear elastic solution into the nonlinear homogeneous constitutive equation.
- Rocket Propellants