Two-scale constitutive modeling of a lattice core sandwich beam

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.

Two-scale micropolar plate model for web-core sandwich panels

“…We note that there are different strategies to obtain the periodic, classical 3-D stresses of a web-core sandwich panel by post-processing the 2-D micropolar results. For web-core beams this was done in (Karttunen et al, 2019) and for full 3-D web-core panels this will be carried out in future studies. Finally, this study introduced a theoretical micropolar plate model which can be used as the basis for micropolar finite element developments similar to those presented by Ansari et al (2017bAnsari et al ( , 2018.…”

“…Figure 2 shows, for modeling purposes, a web-core unit cell attached to an arbitrary fiber of a micropolar plate; see the dashed line along z-axis for the fiber. This situation is analogous to a case in which a unit cell is attached to an arbitrary cross section of a micropolar beam (Karttunen et al, 2019). The 2-D micropolar continuum plate as a whole is a macrostructure and the discrete 3-D unit cell represents its periodic microstructure.…”

“…Recently, analytical solutions founded on discrete classical models have also been formulated for web-core plates Bhaskar, 2016, 2017;Pydah and Batra, 2018). As for the different ESL-FSDT beam models, it has been shown that only the micropolar approach can capture accurately the deformations of a web-core beam because it considers both symmetric and antisymmetric shear and local bending deformations (Karttunen et al, 2018a(Karttunen et al, , 2019. This is explained schematically in Fig.…”

Nonlinear finite element analysis of lattice core sandwich beams

“…In this section, we consider four different lattice material sandwich beam cores, namely, the web-core studied earlier in the linear context (Karttunen et al, 2018b) and the hexagonal, Y-frame and corrugated cores presented in Fig. 2.…”

On the multi-scale vibroacoustic behavior of multi-layer rectangular core topology systems

“…Moreover, Mazloomi et al [6] obtained a great reduction of the sound insulation constructing the sandwich panel by combining a mixture of different in-plane cores, made of different geometries ranging gradually from hexagonal to auxetic. In addition to honeycomb cores, several studies are carried out on web cores focusing their research on acoustic properties [7,8] or the bending and the vibration behavior [9,10], more specifically for building applications. Such studies still remain limited in terms of exploration of geometrical parameters and design proposals since only a single core is considered.…”