A combined r-h adaptive strategy based on material forces and error assessment for plane problems and bimaterial interfaces

Abstract

An r-h adaptive scheme has been proposed and formulated for analysis of bimaterial interface problems using adaptive finite element method. It involves a combination of the configurational force based r-adaption with weighted laplacian smoothing and mesh enrichment by h-refinement. The Configurational driving force is evaluated by considering the weak form of the material force balance for bimaterial inerface problems. These forces assembled at nodes act as an indicator for r-adaption. A weighted laplacian smoothing is performed for smoothing the mesh. The h-adaptive strategy is based on a modifed weighted energy norm of error evaluated using supercovergent estimators. The proposed method applies specific non sliding interface strain compatibility requirements across inter material boundaries consistent with physical principles to obtain modified error estimators. The best sequence of combining r- and h-adaption has been evolved from numerical study. The study confirms that the proposed combined r-h adaption is more efficient than a purely h-adaptive approach and more flexible than a purely r-adaptive approach with better convergence characteristics and helps in obtaining optimal finite element meshes for a specified accuracy.

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Correspondence to S. M. Sivakumar.

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Rajagopal, A., Sivakumar, S.M. A combined r-h adaptive strategy based on material forces and error assessment for plane problems and bimaterial interfaces. Comput Mech 41, 49–72 (2007). https://doi.org/10.1007/s00466-007-0168-8

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Keywords

  • Configurational forces
  • Optimal meshes
  • r-h adaptivity
  • Error estimation
  • Bimaterial interfaces