Premium
Multi‐level h p ‐adaptivity for cohesive fracture modeling
Author(s) -
Zander Nils,
Ruess Martin,
Bog Tino,
Kollmannsberger Stefan,
Rank Ernst
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5340
Subject(s) - finite element method , discretization , a priori and a posteriori , computer science , displacement (psychology) , fracture mechanics , path (computing) , degrees of freedom (physics and chemistry) , stress (linguistics) , algorithm , fracture (geology) , structural engineering , mathematics , materials science , mathematical analysis , engineering , physics , psychology , philosophy , linguistics , epistemology , quantum mechanics , composite material , psychotherapist , programming language
Summary Discretization‐induced oscillations in the load–displacement curve are a well‐known problem for simulations of cohesive crack growth with finite elements. The problem results from an insufficient resolution of the complex stress state within the cohesive zone ahead of the crack tip. This work demonstrates that the hp ‐version of the finite element method is ideally suited to resolve this complex and localized solution characteristic with high accuracy and low computational effort. To this end, we formulate a local and hierarchic mesh refinement scheme that follows dynamically the propagating crack tip. In this way, the usually applied static a priori mesh refinement along the complete potential crack path is avoided, which significantly reduces the size of the numerical problem. Studying systematically the influence of h ‐refinement, p ‐refinement, and h p ‐refinement, we demonstrate why the suggested h p ‐formulation allows to capture accurately the complex stress state at the crack front preventing artificial snap‐through and snap‐back effects. This allows to decrease significantly the number of degrees of freedom and the simulation runtime. Furthermore, we show that by combining this idea with the finite cell method, the crack propagation within complex domains can be simulated efficiently without resolving the geometry by the mesh. Copyright © 2016 John Wiley & Sons, Ltd.