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arXiv · 1810.06385

Two-scale constitutive modeling of a lattice core sandwich beam

Anssi T. Karttunen·JN Reddy·Jani Romanoff
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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.

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Anssi T. Karttunen, JN Reddy, Jani Romanoff. 2018-10-18. Two-scale constitutive modeling of a lattice core sandwich beam. https://doi.org/10.1016/j.compositesb.2018.09.098

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