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Analytical integration of the tractions induced by non-singular dislocations on an arbitrary shaped triangular quadratic element

Journal Article · · Modelling and Simulation in Materials Science and Engineering
 [1];  [1];  [1];  [2];  [2]
  1. Univ. Sorbonne Paris Nord, Villetaneuse (France)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
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Here, an analytical model is proposed to evaluate the nodal force induced by a segment of dislocation upon an arbitrary shaped triangular element. This calculation is required in hybrid methods that associate dislocation dynamics to boundary or finite element to solve simultaneously the evolution of large ensembles of dislocations with complex boundary conditions. Nodal forces are defined as the triple integration of the unbalanced traction field induced by a straight dislocation upon the surface of the element. Following our previous approach (Queyreau et al 2014 Modelling Simul. Mater. Sci. Eng. 22 035004) on a simpler geometry and in the case of linear isotropic elasticity, triple integrals are solved by sequences of integration by parts that exhibit recurrence relations. The traction field is defined and finite everywhere even at the core of dislocations, thanks to the use of the non-singular stress expression formulated by Cai et al (2006 J. Mech. Phys. Solids 54 561–587). The nodal force expressions can be used when considering both a single convolution or double convolution of the Green's function with the core distribution. A solution is also proposed for the case of a semi-infinite segment through the study of the asymptotic behavior of the analytical expressions. The proposed approach is exact and very computationally efficient. The choice of an arbitrary shaped triangular element and quadratic shape functions allow the consideration of complex geometries and comply with automatic meshing procedures. These analytical expressions could also be employed to estimate dislocation interactions with interfaces.
Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1659394
Alternate ID(s):
OSTI ID: 23104816
Report Number(s):
LLNL-JRNL--789620; 987924
Journal Information:
Modelling and Simulation in Materials Science and Engineering, Journal Name: Modelling and Simulation in Materials Science and Engineering Journal Issue: 7 Vol. 28; ISSN 0965-0393
Publisher:
IOP PublishingCopyright Statement
Country of Publication:
United States
Language:
English

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