A GENERALIZED FICTITIOUS CRACK MODEL-BASED ON PLASTIC LOCALIZATION AND DISCONTINUOUS APPROXIMATION

Modelling of crack behaviour is an important topic when establishing r ealistic macroscopic constitutive relations for brittle materials, suc h as ceramics, concrete, rock, etc. Upon introducing discontinuous app roximation of the continuum, a crack model is derived on the basis of the Rankine plasticity model and the fictitious crack concept of Hille rborg et al.(1) The derivation results in a crack band relation, whose constitutive properties are based on failure kinematics that resemble the classical shear band concept. It appears that it is, essentially, the acoustic tenser that governs the constitutive relation for the cr ack band. This tenser has previously been analysed extensively to dete rmine conditions for loss of ellipticity and possibility for discontin uous bifurcation in the rate of deformation field. In the present appr oach a similar analysis is carried out to determine conditions that ch aracterize fracture initiation and crack band orientation. The model i s implemented together with a mesh realignment strategy, and a solutio n advancement formulation, that ensures the crack propagates along cri tical interfacial directions. These directions depend on the actual st ress state and are kept fixed after plastic localization (or cracking) has occurred. Hence, a 'fixed crack' model is obtained. Numerical res ults involving successive crack development as well as failure of conc rete beams are presented.