Continuous/discrete strategies for the modelling of fracturing solids

摘要

Computational strategies involved in the numerical simulation of large scale practical problems, characterised by a transition from a continuum to a discontinuous state, are reviewed in the present work. For problems restricted to relatively small deformations, the use of continuum based methods may be suitable, but for situations involving large geometric changes with possible post-fracture particle flow, there are compelling advantages in employing combined finite/discrete element solution strategies. The need for rigorous consideration of both theoretical and algorithmic issues is emphasised, particularly in relation to the computational treatment of the progressive damage that precedes crack initiation and element technology capable of dealing with plastic incompressibility. Other important aspects such as adaptive mesh refinement procedures are discussed and attention is given to choice of appropriate error estimators which are able to capture internal deterioration of the material. Finally, procedures are presented for undertaking the transition from continuously distributed fracture states to discrete crack systems, followed by post-failure modelling. Issues that are addressed in this context include mesh objectivity requirements, discrete element modelling, procedures for detecting the interaction between large systems of discrete objects and the imposition of specific interaction/contact laws. The practical application of the above methodology is illustrated by the numerical solution of relevant problems.