Discrete Versus Smeared Crack Analysis

Recent developments in numerical analysis of cracking are briefly reviewed and summarized. 1. Recent Developments in the Analysis of Cracking the recent past a number of exciting developments have changed the field of failure analysis by reconciling in part the fundamental differences between plasticity and fracture. The formation of discon- tinuities, which has been addressed within the framework of local- ization analysis at constitutive level, has made significant progress through analytical solutions. They are available for a wide spectrum of plasticity and damage formulations based on loading functions. Recent advances in spectral analysis of rank-one updates have essen- tially resolved the detection of singularities due to localization [22,23]. Moreover, the geometric interpretation of these singularities in terms of Mohr coordinates has added valuable insight into the formation of continuous and discontinuous failure modes and orientation [33]. The basic differences of failure analysis really start at that point, when weak and strong discontinuities initiate at the material level. 1885 simple classification into discrete and smeared concepts does no A....,AA-'"'~ do justice to multitude of failure analysis approaches. discrete crack and its extension with linear and nonlinear fracture mechanics has been replaced in concrete mechanics by the fictitious concept [9], and physical manifestation in terms of decohe- frictional interface contact [27,4,35-40]. The shortcomings of fixed orthotropic concept [20,24] in smeared failure analy- been improved considerably by rotating crack and multicrack concepts [15,7,2,41] . Another layer of complexity was recently added to the anisotropic smeared crack formulation by the microplane for- mulation [42,43] which projects material degradation on a finite num- ber of 'microplanes' onto the continuum level via kinematic constraint and energy arguments.