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REVIEW ARTICLES: Failure Modes in Dynamic Fracture

Stability and Imperfections in Quasistatic Viscoplastic Solutions

[+] Author and Article Information
T. Belytschko, B. Moran, M. Kulkarni

Department of Civil Engineering, Northwestern University, Evanston, Illinois 60208, U.S.A.

Appl. Mech. Rev 43(5S), S251-S255 (May 01, 1990) doi:10.1115/1.3120819 History: Online April 30, 2009

Abstract

The effect of imperfections on the structure of shear bands in strain-softening viscoplasticity is studied via a closed form solution. The stability of various solutions is then examined by varying the data through imperfections. It is shown that a step-function imperfection, such as commonly used in finite element solutions, leads to a step-function shear strain field, which is an unstable solution. Arbitrary C0 and C1 imperfections lead to C0 and C1 strain fields, respectively. Fourier analyses show that the imperfection scales the response of the viscoplastic material: the Fourier spectrum of the strain field is strongly influenced by the Fourier spectrum of the imperfection.

Copyright © 1990 by American Society of Mechanical Engineers
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