**About this Abstract** |

**Meeting** |
**2018 TMS Annual Meeting & Exhibition
** |

**Symposium
** |
**Algorithm Development in Materials Science and Engineering
** |

**Presentation Title** |
Three Dimensional Trefftz Voronoi Cell Finite Elements with Cylindrical Elastic/Rigid Inclusions &/or Voids for Micromechanical Modeling of Heterogeneous Materials |

**Author(s)** |
Guannan Wang, Leiting Dong, Satya N Atluri |

**On-Site Speaker (Planned)** |
Guannan Wang |

**Abstract Scope** |
Three-dimensional Trefftz Voronoi Cell Finite Elements are extended for the micromechanical modeling of heterogeneous materials with embedded elastic/rigid cylindrical inclusions or voids. The present model differs from the previous VCFEMs in the sense that a compatible displacement field is firstly assumed in Barycentric coordinates as nodal displacements, the trial displacement fields of both matrix and inclusion within the element are then developed using Papkovich-Neuber solutions, following the Trefftz method’s framework, which automatically satisfy the Navier’s equations and compatibilities. Cylindrical harmonics are then developed to represent the Papkovich-Neuber potential. A characteristic length is introduced to rescale the ill-conditioned functions in the cylindrical harmonics. Collocation technique is employed to apply the continuity conditions and node-element displacement relationship, and a primal variational principle is derived to establish the element stiffness matrix. Finally, several numerical examples are then illustrated to prove the accuracy of the present model. |

**Proceedings Inclusion?** |
Planned: Supplemental Proceedings volume |