CHEN Xi, ZHANG Jian, LIU Jian-kun. An Explicit Sub-Stepping Stress Integration Method and Its Applications in Numerical Simulations of SMA[J]. Applied Mathematics and Mechanics, 2013, 34(6): 576-585. doi: 10.3879/j.issn.1000-0887.2013.06.004
Citation: CHEN Xi, ZHANG Jian, LIU Jian-kun. An Explicit Sub-Stepping Stress Integration Method and Its Applications in Numerical Simulations of SMA[J]. Applied Mathematics and Mechanics, 2013, 34(6): 576-585. doi: 10.3879/j.issn.1000-0887.2013.06.004

An Explicit Sub-Stepping Stress Integration Method and Its Applications in Numerical Simulations of SMA

doi: 10.3879/j.issn.1000-0887.2013.06.004
  • Received Date: 2013-01-18
  • Rev Recd Date: 2013-05-15
  • Publish Date: 2013-06-15
  • Shape memory alloy (SMA) has complex thermomechanical constitutive relation, thus its numerical simulations demand reliable and efficient stress integration algorithms. The implicit returnmapping stress point algorithms, which have been successfully applied to such materials, may encounter convergence difficulties when loading conditions are complicated or load steps are large. Hence, an explicit substepping stress integration method with automatic local error control was proposed for the simulation of the thermomechanical constitutive relation of shape memory alloys. By investigating several numerical examples, the efficiency of the proposed method and the implicit returnmapping stress point algorithm were evaluated and compared. Numerical results indicate that the number of global sub-steps dominates the entire analyzing time for large-scale computations.The proposed modified Euler automatic sub-stepping scheme leads to less global sub-steps so that the computing time is significantly reduced. Therefore, the explicit sub-stepping stress integration method has the potential for large-scale SMA simulations and computations.
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