ISSN:
0029-5981
Keywords:
plasticity
;
discontinuity
;
regularization
;
interface relation
;
crack band
;
mesh realignment
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
Modelling of crack behaviour is an important topic when establishing realistic macroscopic constitutive relations for brittle materials, such as ceramics, concrete, rock, etc. Upon introducing discontinuous approximation of the continuum, a crack model is derived on the basis of the Rankine plasticity model and the fictitious crack concept of Hillerborg 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 tensor that governs the constitutive relation for the crack band. This tensor has previously been analysed extensively to determine conditions for loss of ellipticity and possibility for discontinuous bifurcation in the rate of deformation field. In the present approach a similar analysis is carried out to determine conditions that characterize fracture initiation and crack band orientation. The model is implemented together with a mesh realignment strategy, and a solution advancement formulation, that ensures the crack propagates along critical interfacial directions. These directions depend on the actual stress state and are kept fixed after plastic localization (or cracking) has occurred. Hence, a ‘fixed crack’ model is obtained. Numerical results involving successive crack development as well as failure of concrete beams are presented.
Additional Material:
12 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620381809
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