Numerical Solutions of Initial-Boundary-Value Problems with Shear Strain Localization

  • R. C. Batra
Part of the International Centre for Mechanical Sciences book series (CISM, volume 386)


The article summarizes some of the results obtained numerically since 1984 by the author and his colleagues on one (simple shearing), two (plane strain and axisymmetric) and three (twisting of a thin-walled and a thick-walled tube) dimensional adiabatic shear banding problems in thermoviscoplastic materials. The material models considered account for strain and strain rate hardening, thermal softening, dipolar effects with the second order spatial gradients of the velocity field taken as independent kinematic variables and the corresponding higher order stresses as kinetic variables, and the nucleation, growth and coalescence of voids. The effect of phase transformation and the consequent change in the material properties has also been accounted for. Different shapes and types of defects considered include geometric such as the variation in the thickness, rigid inclusions, voids, nonuniform initial conditions, and weak elements. Some of the problems studied where no a priori defect is introduced to nucleate a shear band include the plane strain compression of a FCC single crystal, the Taylor impact test, and the penetration of a tungsten heavy alloy or a depleted uranium rod into a steel target.


Shear Band Slip System Adiabatic Shear Band Effective Plastic Strain Plane Strain Compression 
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© Springer-Verlag Wien 1998

Authors and Affiliations

  • R. C. Batra
    • 1
  1. 1.Virginia Polytechnic Institute and State UniversityBlacksburgUSA

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