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Strain localization and bifurcation in a nonlocal continuum. (English) Zbl 0799.73005

The authors address the problem of the strain-softening which renders localization instabilities and ill-posedness of boundary value problems. Using the three-dimensional damage control model, the rate constitutive relations for the linear comparison solid are derived, and conditions for bifurcation from a homogeneous state are obtained. A comparison is given with the localization analyses in a usual medium. In the dynamic case similar analysis is used to conclude that wave propagation in the nonlocal continuum is dispersive.

MSC:

74A30 Nonsimple materials
74R99 Fracture and damage
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