Stability against Localization of Softening into Ellipsoids and Bands: Parameter Study

Strain-iocalimtion instabilities due to strain-softening which result from distributed damage such (IS cracking in heterogeneous brittle materials are analyzed. Attention is restricted to the stability problem of equilibrium states. This problem is not equivalent to bifurcation of the equilibrium path. which may occur before stability of Lquilibrium is lost. The continuum is local but is enhunccd by the localization limiter used in the crack hand model. consisting of a lower bound on the minimum dimension of the strain-localization region. which is regarded as a material property. Presented arc derivations of the critical state conditions for localizttion of initially uniform strain into ellipsoidal domains within an infinite continuum and into a planar band within a layer of linitc thickness. Thcsc dcrivnlions arc simpler than the previous Bahnt’s dcrivalions of the gcncral stability conditions for thcsc Iocalizations. A numerical paramctcr study of the critical states is made for a broad range of mat&al properties as well as various initial slrcss statcs and rclativc sixs of the strain-softening region. The material is dcscribcd by Druckcr Pragcr plasticity with strain-roftcning that is rauscd hy yield limit degradation. Tlls Ilattcr the ellipsoidal domain, or the Iargcr the six of tbc holy (Iaycr thickness). thc_smallcr is found to be the strain-softening slope magnitude at which the critical state is rcarhcd. A softening Druckcr Pragcr material is found to bc stahlc against plauar-hand localibations in inlinitc continuum for a certain range of softening material paranictcrs.