SUMMARYThis paper is concerned with the development of a numerical algorithm for the solution of the uncoupled, quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation. The constitutive equations, expressed in integral form involving the relaxation moduli, are transformed into an incremental algebraic form prior to development of the ÿnite element formulation. This incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the ÿnite element solution. Use is made of a Dirichlet-Prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory. Three illustrative example problems are included to demonstrate the method.
The influence of texture on the spallation (Hopkinson fracture) of low-symmetry metals (e.g. Zr, U, or Sn) has seen limited study. In this study, the Hopkinson fracture of annealed, high-purity Zr has been probed as a function of crystallographic texture. The quasi-static yield strength of the Zr studied is ≈2.5x higher in the plate's through-thickness direction compared to that measured in-plane due to a pronounced basal texture. The pullback signals of each orientation shocked to 5 GPa were found to be insensitive to the texture, although the HEL's and the soft-recovered, incipiently-spalled samples exhibited differences in their damage evolution. The VISAR wave profiles were modeled using a 3-D finite-volume method (FVM) continuum code. The VISAR, post-spallation metallographic observations, and modeling analysis are discussed with reference to the HEL and texture.
Density-functional theory is used to calculate unit-cell energies of ␣-Pu and ␦-Pu lattices containing point defects that are manifest in terms of a contaminant He atom. These cell energies are used in the development of a new exp− 6 Pu-He interatomic potential. Molecular-dynamics simulations are conducted to investigate the dynamics of individual He atoms and of a cluster of He atoms in a ␦-Pu lattice. In both cases, the He atoms are shown to precipitate chain reactions involving split interstitial migration of Pu. The rate of this split interstitial migration is calculated. Molecular dynamics is also used to investigate the dynamics of an isolated He bubble in a ␦-Pu lattice. Questions concerning the stability of a He bubble possessing a He-to-vacancy ratio of 3:1 are investigated. Molecular-dynamics simulations investigating the evolution of bubble shape over time are carried out.
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