A method for dynamic crack and shear band propagation with phantom nodes

TLDR

The study introduces a new method for modelling arbitrary dynamic crack and shear band propagation. The method employs a rearranged extended finite element basis with phantom nodes and superposed elements, adds phantom degrees of freedom for shear bands, and uses a single‑point quadrature with hourglass control for 4‑node quadrilaterals. This approach simplifies element‑by‑element crack and shear band propagation in explicit simulations, yields consistent history variables without subdomain integration, and is shown to be effective and robust in numerical examples. © 2006 John Wiley & Sons, Ltd.

Abstract

Abstract A new method for modelling of arbitrary dynamic crack and shear band propagation is presented. We show that by a rearrangement of the extended finite element basis and the nodal degrees of freedom, the discontinuity can be described by superposed elements and phantom nodes. Cracks are treated by adding phantom nodes and superposing elements on the original mesh. Shear bands are treated by adding phantom degrees of freedom. The proposed method simplifies the treatment of element‐by‐element crack and shear band propagation in explicit methods. A quadrature method for 4‐node quadrilaterals is proposed based on a single quadrature point and hourglass control. The proposed method provides consistent history variables because it does not use a subdomain integration scheme for the discontinuous integrand. Numerical examples for dynamic crack and shear band propagation are provided to demonstrate the effectiveness and robustness of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.