Verification and validation of multiscale fracture in ceramics by discretization and model adaptivity

• Applicant: Professor Dr.-Ing. Peter Wriggers
• Subject Area: Mechanics
• Term: from 2009 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 117309069

• Final Report Year: 2014

Final Report Abstract

In this research project we proposed, elaborated and implemented a new unified, simple, affordable and reliable error-controlled adaptive computational approach for prediction of microstructural crack initiation and propagation, based on modeling of C1-continua, resulting in macrocracks in the frame of brittle elastic theory for ceramics (zirconium oxide), followed by their progression paths and eventually the failure of a structural component. Damage development on micro-scale of ceramic material, micro-crack initiation and propagation is analyzed by adaptive FEM using a new explicit residual error estimator which has the pronounced advantages that it provides guaranteed computable upper bound with effectivity indices between 1 and 2, what is treated as practically (very) acceptable. Non-local damage analysis is applied to identify areas where nucleation of cracks is expected, followed by transition from continuous damage to equivalent micro-cracks, using energetic equivalence between damage and fracture. Progression of macro-cracks within linear elastic fracture mechanics is realized both by adaptive eXtended and classical (not extended) FEMs, using new explicit and implicit error estimators. Important results are: (1) The numerical analysis of crack propagation on micro and macro scales requires error-controlled adaptive remeshing in the frame of classical FEM. Otherwise, the paths of crack propagation are erroneous. (2) With the use of triangular and tetrahedral finite elements, mesh adaptivity for progressing cracks is very efficient, especially by using the new explicit residual error estimator with upper bound property. (3) Micro-crack opening modeled by preceding non-local damage analysis (using enhanced gradients) yields non-unique solutions in case of several singular stress concentrations within a specimen; experiments show that a crack begins only at one of those singularities. Therefore, further model adaptivity for crack initiation is indicated, especially by using molecular dynamics.

Publications

• Explicit and implicit residual-type goal-oriented error estimators for XFEM in LEFM, In D. Aubry et al., editors, Adaptive modeling and simulation 2011, ECCOMAS Thematic-Conference Paris 2011, pages 44–55. CIMNE, Barcelona, 2011
  E. Stein, T. Gerasimov, and M. Rüter
  
• An explicit residual-type error estimator for Q1-quadrilateral XFEM in 2D LEFM. Int. J. Numer. Meth. Engng., 90(9):1118–1155, 2012
  T. Gerasimov, M. Rüter, and E. Stein
  
• Adaptive FEM, XFEM and SFM for Damage and Fracture of brittle elastic Materials at Micro- and Macro-Scales. XX. Computer Methods in Mechanics (CMM) 2013, Poznan, Poland, 27–31 August 2013
  E. Stein, T. Gerasimov, and P. Wriggers
  
• Error-controlled adaptive multiscale analysis for crack initiation and propagation in brittle materials, in: Adaptive Modeling and Simulation (ADMOS) 2013, VI. International Conference, Lisbon, Portugal, 3 – 5 June 2013, p. 24
  E. Stein, T. Gerasimov, and M. Rüter
  
• Goal-oriented explicit residual-type error estimates in XFEM. Comput. Mech., 52(2):361–376, 2013
  M. Rüter, T. Gerasimov, and E. Stein
  (See online at https://doi.org/10.1007/s00466-012-0816-5)
• The constant-free explicit error estimator with sharp upper error bound property for adaptive FE analysis in elasticity and fracture. IJNME, 20 October 2014
  T. Gerasimov, E. Stein, and P. Wriggers
  (See online at https://doi.org/10.1002/nme.4768)