Two-scale constitutive modeling of a lattice core sandwich beam

TL;DR

This paper develops a two-scale constitutive model for a lattice core sandwich beam using a micropolar Timoshenko beam approach, linking microscale unit cell behavior to macroscale beam responses for static and dynamic analysis.

Contribution

It introduces a novel two-scale modeling method that derives 1-D constitutive equations from microscale lattice unit cells for web-core sandwich beams.

Findings

Localized 1-D model results agree with experimental data.

The model accurately predicts static and dynamic behavior.

Efficient analysis of complex sandwich panels is enabled.

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.