Mesh refinement strategies without mapping of nonlinear solutions for the generalized and standard FEM analysis of 3-D cohesive fractures

J. Kim, A. Simone, C. A. Duarte

Research output: Contribution to journalArticlepeer-review

Abstract

A robust and efficient strategy is proposed to simulate mechanical problems involving cohesive fractures. This class of problems is characterized by a global structural behavior that is strongly affected by localized nonlinearities at relatively small-sized critical regions. The proposed approach is based on the division of a simulation into a suitable number of sub-simulations where adaptive mesh refinement is performed only once based on refinement window(s) around crack front process zone(s). The initialization of Newton-Raphson nonlinear iterations at the start of each sub-simulation is accomplished by solving a linear problem based on a secant stiffness, rather than a volume mapping of nonlinear solutions between meshes. The secant stiffness is evaluated using material state information stored/read on crack surface facets which are employed to explicitly represent the geometry of the discontinuity surface independently of the volume mesh within the generalized finite element method framework. Moreover, a simplified version of the algorithm is proposed for its straightforward implementation into existing commercial software. Data transfer between sub-simulations is not required in the simplified strategy. The computational efficiency, accuracy, and robustness of the proposed strategies are demonstrated by an application to cohesive fracture simulations in 3-D.

Original languageEnglish (US)
Pages (from-to)235-258
Number of pages24
JournalInternational Journal for Numerical Methods in Engineering
Volume109
Issue number2
DOIs
StatePublished - Jan 13 2017

Keywords

  • Newton-Raphson method
  • adaptive mesh refinement
  • cohesive fracture
  • generalized finite element method
  • three-dimensional simulation

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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