Shear flow localization in thermoviscoplastic materials and a numerical study of dynamic problems in continuous media
In the present work, three problems are considered. The first problem is concerned with the study of shear-flow localization in thermoviscoplastic materials in the setting of a one-dimensional simple shearing of an infinite plate subjected to constant-velocity boundary conditions. Both the isothermal and adiabatic boundary conditions are considered and localization is assumed to be triggered by either geometric or temperature imperfections in the body. A localization criterion based on the evolution of the total kinetic energy is proposed and used in comparing the susceptibilities of various engineering materials to localization. Further, the completion of localization is identified with the attainment of a maximum in the plastic strain rate at the center of the band. Several numerical experiments are conducted to study the influence of dissipation, diffusion and inertia on localization. The validity of such assumptions as negligible inertia and adiabatic deformation is examined. Also, the validity of the classical Fourier's law is explored through a modification to the Fourier's equation. In addition, the possibility of localization due to the inhomogeneity of the material structure is studied by considering the simple shearing of a multilayered plate made of two different materials. In the second part of the present work, an accurate finite difference scheme is presented for the propagation of elastic waves in a thick disk subjected to traction boundary conditions. One face of the disk is subjected to an impact load while the rest of the surface is traction-free. A stability condition based on the classical von Neumann analysis is also derived. The numerical results compare excellently with analytical results from a modal analysis. Finally, in the third part of the present work, the dispersion characteristics of a non-dissipative scheme for wave propagation problems in continuous media is studied.
Engineering, Civil, Engineering, Mechanical, Engineering, Materials Science
University of Illinois - Urbana-Champaign
Networked Digital Library of Theses and Dissertations
University of Illinois at Urbana-Champaign