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

Pijaudier-Cabot, Gilles; Benallal, Ahmed

Int. J. Solids Struct. 30, No. 13, 1761-1775 (1993).

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.

Reviewer: F.D.Zaman (Dhahran)

MSC:

74A30	Nonsimple materials
74R99	Fracture and damage

Keywords:

strain-softening; ill-posedness; boundary value problems; damage control model; wave propagation