A Physical Model and Conservation Equations for Dynamic Solid-Liquid Behavior.
Abstract
A self-consistent set of equations were developed for 3-D penetration problems. The set of equations includes polymorphic and thermodynamic phase changes, finite material extensions and rotations between time-steps, thermal softening, Hugioniot volumetric relationships, strain and strain-rate dependency for elastic-viscoplastic deviatoric behavior, generalized inertial forces, and conductive, convective and radiation heat fluxes. Continuous mapping between fluid and solid states were obtained by selecting velocity and temperature as the primary variables. The resulting set of mass, linear momentum and energy equations form a coupled set of differential and integral-differential equations. These equations were approximated by discretizing in both time and space via the method of weighted residuals using piecewise continuous weighting and trial functions. A quadratic time-element was assumed and a wide variety of algebraic recursion relationships were derived for the corresponding implicit solution schemes. In order to quickly evaluate any of these solution schemes, a new concept entitled creation and annihilation was introduced where geometric sub-regions are added to, and subtracted from, the geometric problem during the penetration process. Keywords: Constitutive equations, Finite elements, Fluid mechanics, Nonlinear Mechanics, Numerical methods, Penetration mechanics, Solid mechanics, Solution techniques.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1986
- Accession Number
- ADA165295
Entities
People
- John N. Majerus
Organizations
- Villanova University