Computational Mechanics

, Volume 52, Issue 6, pp 1265–1279 | Cite as

Concurrent multiresolution finite element: formulation and algorithmic aspects

  • Shan Tang
  • Adrian M. Kopacz
  • Stephanie Chan O’Keeffe
  • Gregory B. Olson
  • Wing Kam LiuEmail author
Original Paper


A multiresolution concurrent theory for heterogenous materials is proposed with novel macro scale and micro scale constitutive laws that include the plastic yield function at different length scales. In contrast to the conventional plasticity, the plastic flow at the micro zone depends on the plastic strain gradient. The consistency condition at the macro and micro zones can result in a set of algebraic equations. Using appropriate boundary conditions, the finite element discretization was derived from a variational principle with the extra degrees of freedom for the micro zones. In collaboration with LSTC Inc, the degrees of freedom at the micro zone and their related history variables have been augmented in LS-DYNA. The 3D multiresolution theory has been implemented. Shear band propagation and the large scale simulation of a shear driven ductile fracture process were carried out. Our results show that the proposed multiresolution theory in combination with the parallel implementation into LS-DYNA can capture the effects of the microstructure on shear band propagation and allows for realistic modeling of ductile fracture process.


Concurrent multiresolution Multiscale Finite element method Heterogenous microstructure 



The support of this work by DARPA-D3D program and NSF CMMI 0823327 is gratefully acknowledged. Discussion with Tobias Erhart and Thomas Borrval in LSTC Inc is greatly acknowledged. WKL was partial supported by the World Class University Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology. The authors also thank John Moore for proof reading and David Chen for help on large scale computing setting on QUEST cluster at Northwestern University. Discussion with Tobias Erhart and Thomas Borrval in LSTC Inc is greatly acknowledged.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Shan Tang
    • 1
    • 2
  • Adrian M. Kopacz
    • 2
  • Stephanie Chan O’Keeffe
    • 3
  • Gregory B. Olson
    • 3
  • Wing Kam Liu
    • 2
    • 4
    Email author
  1. 1.College of Material Science and EngineeringChongqing UniversityChongqingChina
  2. 2.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA
  3. 3.Department of Material Science and EngineeringNorthwestern UniversityEvanstonUSA
  4. 4.School of Mechanical Engineering, World Class University (WCU) ProgramSungkyunkwan UniversitySeoulKorea

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