Simulated Properties of Kagomé and Tetragonal Truss Core Panels

TLDR: In this paper, the finite element method has been used to simulate the properties of panels with Kagome and tetragonal cores under compressive and shear loading, and the simulation has been performed for two different materials: a Cu-alloy with extensive strain hardening and an Al-aloy with minimal hardening.

About: This article is published in International Journal of Solids and Structures.The article was published on 2003-12-01 and is currently open access. It has received 195 citations till now. The article focuses on the topics: Strain hardening exponent & Tetragonal crystal system.

Figures

Fig. 4. The tetragonal (a) and Kagome (b) configurations made from Cu alloys under compression at an imposed strain, D=H ¼ 0:05, beyond the load maximum. Note that, for both cores, the trusses experience plastic buckling.

Fig. 3. Non-dimensional force/strain curves calculated in compression for tetragonal and Kagome cores made from (a) Cu alloy and (b) Al alloy.

Table 1 Plastic buckling strengths (rpb) for the truss members (MPa)

Fig. 5. Unload/reload simulations (Cu alloy) revealing that, for the tetragonal core (a), the unloading modulus decreases at strains beyond the onset of plastic buckling. For the Kagome core (b), the modulus maintains virtually constant through the same dis placements.

Fig. 8. Unload/reload simulations for the tetragonal core (a) and Kagome core (b) in shear orientation I.

Fig. 6. Non-dimensional force/strain curves calculated in three shear orientations for the tetragonal and Kagome cores made from Cu (a,b) and Al (c,d) alloys.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Simulated properties of kagomé and tetragonal truss core panels" ?

How does access to this work benefit you ? Publisher 's Statement NOTICE: this is the author ’ s version of a work that was accepted for publication in International Journal of Solids and Structures. Changes may have been made to this work since it was submitted for publication. 

Q2. Why were the small displacement increments selected?

Small displacement incre ments, D, were selected, especially near yield, to avoid numerical instability and the occurrence of local minima (D=H ranged from 0.003 to 0.025, where H is the core height). 

Q3. What is the maximum load of the tetragonal core?

Responses of both structures are initially iso tropic, but only the Kagome core maintains the isotropy after yielding; it strain hardens and is resistant to plastic buckling in compression and shear. 

Q4. Why are the peak loads lower for the Al alloy than the Cu/Be alloy?

The peak loads are systematically lower for the Al alloy than the Cu/Be alloy, and occur at lower D, because of the differences in strain hardening. 

Q5. What is the loading modulus for the tetragonal core?

The unloading modulus for the tetragonal core decreases in the post-buckling regime, while that for the Kagome core remains the same throughout. 

Q6. What is the displacement-control theory used to simulate the compression and shear of the face sheet?

The simulations were performed subject to displacement-control, using large displacement theory to capture the softening in the post-buckling state. 

Q7. What is the strain hardening exponent for the stress/strain curves?

The stress/strain [rðeÞ] curves are fit to a Ramberg–Osgood representation:e ¼ r=E þ ðrY =EÞðr=rYÞN ; ð2Þwith the strain hardening exponent N . 

Q8. What is the compressive strength of the optimized sandwich panel?

The compressive strength rY c of the optimized sandwich panel is given by (Wicks and Hutchinson, 2000):H 2 c corer =r ¼ q : ð4ÞY Y coreLThe maximum stress needed to crush the core is obtained by using the stress for plastic buckling rpb in Eq. (3), determined for the clamped conditions k ¼ 4, and inserting into the result for the compressive strength (4). 

Q9. What is the genesis of the 3D Kagome?

The genesis of this choice hasbeen the recent finding from topology optimization that 2D Kagome structures are structurally efficient (Hyun and Torquato, 2002). 

Q10. What is the maximum stress needed to crush the tetragonal core and Kagome?

In the simulation, the maximum stresses needed to crush the tetragonal core and Kagome core are given by Pcrush ¼ 4:3 MPa and Pcrush ¼ 5:1 MPa. 

Q11. What is the truss radius and panel height for the Kagome core?

The same truss radius and panel height are used for the Kagome core, but to attain the same core density, the truss length is half that for the tetragonal core (Hyun and Torquato, 2002). 

Q12. What is the strength of the truss material?

This strength relates to the properties of the truss material through the implicit expression:2 N pR -1 rpb rpbk e ¼ þ N ; ð3Þ 2L Y rY rYwhere L is the truss length, with k a measure of the rotational constraint at the junctions (k ¼ 1 when there is no constraint and k ¼ 4 when clamped).