Numerical Integration of a System of Equations in Thermoviscoplasticity.

Abstract

A set of nonlinear and coupled equations governing the thermomechanical deformations of a viscoplastic body undergoing simple shearing deformations is integrated in time by using the Forward-Difference-Galerkin-Finite-Element (FDGFE) method and the Crank-Nicolson-Galerkin-Finite-Element (CNGFE) method. In the latter scheme the number of unknown functions is increased so that the governing equations involve only first order spatial derivatives. It is shown that the solutions obtained by the two methods agree qualitatively but the CNGFE method seems to introduce considerable damping into the system. However, the time increment needed to obtain a stable solution by the CNGFE method is 200 times that required by the FDGFE method. Keywords: Shear bands, Finite element method, Crank nicolson method.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1987
Accession Number
ADA182484

Entities

People

  • Romesh C. Batra
  • Thomas W. Wright

Organizations

  • Ballistic Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies
  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Aeronautical Engineering
  • Air Force
  • Differential Equations
  • Engineering
  • Equations
  • Finite Element Analysis
  • Jet Propulsion
  • Materials
  • Mathematics
  • Mechanical Engineering
  • Mechanics
  • Military Research
  • Partial Differential Equations
  • Shear Bands
  • Shear Stresses
  • Strain Rate
  • War Colleges

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Materials Science and Engineering.
  • Mathematical Modeling and Probability Theory.