Instability of Nonlocal Continuum and Strain Averaging
Publication: Journal of Engineering Mechanics
Volume 110, Issue 10
Abstract
Nonlocal continuum, in which the (macroscopic smoothed‐out) stress at a point is a function of a weighted average of (macroscopic smoothed‐out) strains in the vicinity of the point, are of interest for modeling of heterogeneous materials, especially in finite element analysis. However, the choice of the weighting function is not entirely empirical but must satisfy two stability conditions for the elastic case: (1) No eigenstates of nonzero strain at zero stress, called unresisted deformation, may exist; and (2) the wave propagation speed must be real and positive if the material is elastic. It is shown that some weighting functions, including one used in the past, do not meet these conditions, and modifications to meet them are shown. Similar restrictions are deduced for discrete weighting functions for finite element analysis. For some cases, they are found to differ substantially from the restriction for the case of a continuum if the averaging extends only over a few finite elements.
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Published In
Journal of Engineering Mechanics
Volume 110 • Issue 10 • October 1984
Pages: 1441 - 1450
Copyright
Copyright © 1984 ASCE.
History
Published online: Oct 1, 1984
Published in print: Oct 1984
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