Hierarchical modelling of discontinuous fields

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Abstract
A methodology has been developed to hierarchically model discontinuous fields by means of the s‐version of the finite‐element method. This is achieved by overlaying portions of the finite‐element mesh where discontinuities need to be embedded with a finite‐element mesh which is discontinuous across the crack faces (containing unconstrained double nodes along the discontinuity). By this technique crack propagation can be simulated by advancing the crack front in the superimposed mesh only, keeping the base mesh fixed and unaware of the crack existence. The hierarchical structure of the method ensures computational efficiency, especially in linear systems. Numerical experiments for mode I and mixed‐mode problems are presented to validate the present formulation.

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