Material symmetry and the evolution of anisotropies in first gradient theories of nonlinear material behavior; inelasticity; polymer crystallization

This dissertation is a general theoretical study of modeling material behavior and of how anisotropies (symmetries) change in a material as it undergoes a history of events.;First, the general case is considered where the stress depends on the total history of the deformation gradient (a first-gradient or simple material model). The description of material symmetry, and the factors which influence its change are studied. Not including the particular characteristics of a material, the two main factors which determine how a material changes its symmetries are identified as its initial symmetry properties, and the history of deformations it undergoes. Knowing these two factors, it is shown that one can calculate the minimum symmetry which the material must have after it has undergone a particular process. Finally, for a particular set of deformation histories, this minimum symmetry is calculated for initially isotropic, transversely isotropic, and orthotropic materials.;Particular theories of inelasticity and solid polymer crystallization are considered. For the particular theory of inelasticity used, it is shown that the deformation history influences the response of the material only through the inelastic ("plastic") deformation gradient. The anisotropic-elastic response of the material is shown to depend on the particular value of the inelastic deformation gradient, and on the particular symmetry properties of the inelastic response functional. The type of symmetry associated with the elastic response is given by the eigenvalues of the inelastic strain and the preferred directions are given by its eigenvectors. A detailed description of this theory and the particular dependence mentioned above is presented for an initially isotropic material.;Next, a constitutive equation is developed for isothermal solid polymer crystallization. This constitutive equation, which incorporates the idea of strain induced crystallization, is based on a continuous transition of amorphous to crystalline matter at each point in the material. A detailed description of this model is presented, and a particular form of it is correlated with experimental results for natural rubber crystallization. This model is used to illustrate the possible ways in which such a material's symmetries can change.