Doctoral Dissertations

Date of Award

6-1983

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Engineering Science

Major Professor

Maurice A. Wright

Committee Members

Reddy, Keefer, Maluern

Abstract

Three fundamentally different finite strain constitutive formulations for describing elastic-viscoplastic materials are considered. These are classified as: (1) hyperelastic-viscoplastic, (2) hypolastic-viscoplastic, and (3) updated hyperelastic-viscoplastic. The formulations differ primarily in the kinetic and kinematic quantities used to characterize the material constitutive equations. Objectives are to: (1) establish the theoretical bases of the three constitutive formulations; (2) evaluate the relative numerical efficiency of the material models; (3) determine under what conditions the various descriptions yield comparable results; and (4) develop a computer program which can be used to study finite strain, elastic-viscoplastic constitutive equations in low, intermediate, and high strain rate environments.

The three material models are based on the Perzyna generalization of the Malvern and Sokolovsky viscoplastic over-stress constitutive equations. Although an over-stress model is used, other state-variable constitutive equations may be described using the three constitutive formulations.

The implementation of the three constitutive formulations into a finite element computer program is discussed, and both explicit and implicit methods for integrating the equations of motion and constitutive equations are presented.

Two problems are considered which deal with dynamic plasticity and finite strains. The first problem involves a right circular cylinder impacting a rigid wall (Taylor's cylinder problem), and is dominated by finite dilatational strains while the rotations are small. The second problem is a cantilever beam loaded at its free-end by a triangular-shaped impulse, and involves finite rotations with small dilatational strains.

The results indicate that when the dilatational strains are finite, the hyperelastic-viscoplastic constitutive equation may yield numerical results which differ significantly from those obtained from the hypoelastic-viscoplastic and updated hyperelastic-viscoplastic constitutive equations. When the dilatational strains are small, the three constitutive formulations yield similar numerical results.

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