Computational methods for fracture 1_2 скачать в хорошем качестве

Computational methods for fracture 1_2

Timon RABCZUK: A state-of-the-art overview on computational methods for fracture will be presented. The lecture will discuss especially methods for discrete cracks, i.e. extended meshfree and finite element methods, the phantom node method (a special case of the extended finite element method), extended IGA (Isogeometric analysis) formulations, efficient remeshing techniques and peridynamics (PD). The focus will be on ‘enriched’ methods based on local partition of unity. As an alternative to discrete crack methods, the phase field approach to fracture will be presented which shows similarities to nonlocal or gradient models. The lecture starts with an introduction to meshfree methods (MMs) and different ways to model fracture in MMs. In this context, the concept of intrinsic and extrinsic enrichment schemes based on a local partition of unity will be explained. Subsequently, the extended finite element method (XFEM) for fracture in continua and structures will be addressed. Different enrichment schemes for brittle and ductile failure will be shown. Solutions to difficulties due to blending, enrichment and integration will be given. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, different crack tracking techniques will be discussed. Alternatives to XFEM, in particular extended meshfree methods, the cracking particles methods, the phantom node method and extended IGA formulations will be presented exploiting for example the higher order continuity of meshfree and IGA approximations. One part of the lecture will be dedicated to efficient remeshing techniques that do not require adding degrees of freedom. Subsequently, an overview of peridynamics (PD) will be given which is particularly suitable to model dynamic fracture with numerous cracks and complex fracture patterns. The focus will be on bond-based (BB) and ordinary state based peridynamics. A novel variable horizon peridynamics formulation for adaptive simulation with error control will be presented as well. Finally, the phase field approach including advantages, drawbacks and limitations will be explained as an alternative to discrete crack methods. The lecture will close with a brief overview on cracking criteria for non-linear fracture.