## Abstract

Constitutive equations are derived for a 1-D micropolar Timoshenko beam made of a web-core lattice material. First, a web-core unit cell is modeled by discrete classical constituents, i.e., the Euler–Bernoulli beam finite elements (FE). A discrete-to-continuum transformation is applied to the microscale unit cell and its strain energy density is expressed in terms of the macroscale 1-D beam kinematics. Then the constitutive equations for the micropolar web-core beam are derived assuming strain energy equivalence between the microscale unit cell and the macroscale beam. A micropolar beam FE model for static and dynamic problems is developed using a general solution of the beam equilibrium equations. A localization method for the calculation of periodic classical beam responses from micropolar results is given. The 1-D beam model is used in linear bending and vibration problems of 2-D web-core sandwich panels that have flexible joints. Localized 1-D results are shown to be in good agreement with experimental and 2-D FE beam frame results.

Original language | English |
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Pages (from-to) | 66-75 |

Number of pages | 10 |

Journal | Composites Part B: Engineering |

Volume | 160 |

DOIs | |

Publication status | Published - 1 Mar 2019 |

MoE publication type | A1 Journal article-refereed |

## Keywords

- Constitutive modeling
- Finite element
- Lattice material
- micropolar
- Sandwich structures
- Timoshenko beam