MATERIAL INSTABILITY AND STRAIN-RATE DISCONTINUITIES IN INCREMENTALLY NONLINEAR CONTINUA

被引:42
|
作者
PETRYK, H
机构
[1] Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw
关键词
D O I
10.1016/0022-5096(92)90014-S
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
A SYSTEMATIC analysis of theoretical aspects of material instability is presented for a general class of time-independent, incrementally nonlinear solids which admit a velocity-gradient potential. The second-order energy criteria of instability of uniform straining and of equilibrium are derived for a material element embedded in a quasi-statically deforming continuum. Several theorems concerning propagation of acceleration waves in an incrementally nonlinear material are proved, with particular reference to stationary discontinuities. Initiation of shear band formation either by a dynamic growth of an initial disturbance or by a quasi-static bifurcation is studied as a symptom of material instability. The derived condition for the instability of uniform quasi-static straining does not coincide with that for instability of equilibrium and both differ in general from the familiar condition of strong ellipticity loss formulated for the tangent moduli. This is illustrated on an example of a non-proportional deformation path of material obeying the J2 corner theory of plasticity.
引用
收藏
页码:1227 / 1250
页数:24
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