Computational Modelling of Localisation and Fracture
The computational modelling of failure in a broad class of materials is analysed. Beyond a critical load level deformation may localise in small bands or cracks dependent on the load condition and the properties of the material. The localisation process and fracture have been studied in a finite element framework. The virtual work equation that describes the motion of an inelastic body is discretised and nonlinear solution techniques have been treated. This computational procedure can be used in combination with simple models to describe failure as plasticity, damage and crack models. Localisation is analysed by means of a simple bar analysis and the problem of mesh sensitivity has been explained. To solve this problem enhancement of the plasticity theory is proposed by means of higher-order time derivatives (viscoplastic model) or higher-order spatial derivatives (gradient model). An extensive algorithmic elaboration of all models has been given.
KeywordsYield Surface Integration Point Strain Increment Strain Softening Localisation Zone
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