<p>This paper introduces a novel three-dimensional (3D) architected cellular structure, which was constructed by orthogonally splicing the existing two-dimensional (2D) enhanced honeycomb, and it can also be considered as an enhanced design on the existing common 3D re-entrant lattice structure (CRLS) by embedding a 3D Kagome truss into every cell of it. Analytical models were developed for predicting the Young’s modulus and Poisson’s ratio of the new structure and then verified by the numerical simulations and experiments. A comparison between the new structure and the existing 3D re-entrant lattice structures was carried out. The influences of the micro geometrical parameters on the macro mechanical properties were discussed to fully understand the elastic behavior of the new structure. It is shown that, the relation between the normalized Yong’s modulus, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5589_Article_IEq1.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\hat{E}} \mathord{\left/ {\vphantom {{\hat{E}} {E_{0} }}} \right. \kern-0pt} {E_{0} }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mi>E</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mfenced open="/"> <mphantom> <mpadded width="0pt"> <mover accent="true"> <mi>E</mi> <mo stretchy="false">^</mo> </mover> <msub> <mi>E</mi> <mn>0</mn> </msub> </mpadded> </mphantom> </mfenced> </mrow> <msub> <mi>E</mi> <mn>0</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>, and the relative density, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5589_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\rho^{*} } \mathord{\left/ {\vphantom {{\rho^{*} } {\rho_{0} }}} \right. \kern-0pt} {\rho_{0} }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mi>ρ</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mrow> <mfenced open="/"> <mphantom> <mpadded width="0pt"> <mmultiscripts> <mi>ρ</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <msub> <mi>ρ</mi> <mn>0</mn> </msub> </mpadded> </mphantom> </mfenced> </mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> of the 3D lattice structures follows a simple exponential function, i.e., <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5589_Article_IEq3.gif" Format="GIF" Height="33" Rendition="HTML" Resolution="72" Type="Linedraw" Width="180" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left( {{{\hat{E}} \mathord{\left/ {\vphantom {{\hat{E}} {E_{0} }}} \right. \kern-0pt} {E_{0} }}} \right) = C \cdot \left( {{{\rho^{*} } \mathord{\left/ {\vphantom {{\rho^{*} } {\rho_{0} }}} \right. \kern-0pt} {\rho_{0} }}} \right)^{m}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close=")" open="("> <mrow> <mover accent="true"> <mi>E</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mfenced open="/"> <mphantom> <mpadded width="0pt"> <mover accent="true"> <mi>E</mi> <mo stretchy="false">^</mo> </mover> <msub> <mi>E</mi> <mn>0</mn> </msub> </mpadded> </mphantom> </mfenced> </mrow> <msub> <mi>E</mi> <mn>0</mn> </msub> </mrow> </mfenced> <mo>=</mo> <mi>C</mi> <mo>·</mo> <mmultiscripts> <mfenced close=")" open="("> <mrow> <mmultiscripts> <mi>ρ</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <mrow> <mfenced open="/"> <mphantom> <mpadded width="0pt"> <mmultiscripts> <mi>ρ</mi> <mrow /> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> <msub> <mi>ρ</mi> <mn>0</mn> </msub> </mpadded> </mphantom> </mfenced> </mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> </mrow> </mfenced> <mrow /> <mi>m</mi> </mmultiscripts> </mrow> </math></EquationSource> </InlineEquation>. In the case of CRLS, <i>m</i> tends to 2, while <i>m</i> is close to 1 for the new structure, which reveals that the dominated deformation mode of the CRLS is changed by the embedded struts from bending to stretching. As a result, the new structure has larger specific stiffness with respect to CRLS. Compared to the two existing 3D embedded enhanced re-entrant lattice structures (single rib embedded re-entrant lattice, SRELS, and the spatial rhombic truss embedded lattice structure, SRTELS), the new 3D structure exhibits weaker anisotropy and stronger auxetic effect, which makes the new structure have better application advantages in some specific occasions. This work may provide a good guide for the development of the 3D auxetic lattcie structures with improved mechanical performance.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Equivalent elastic properties of a new stiff 3D auxetic architected cellular structure: analytical prediction

  • Yu Chen,
  • Ziqian Pan

摘要

This paper introduces a novel three-dimensional (3D) architected cellular structure, which was constructed by orthogonally splicing the existing two-dimensional (2D) enhanced honeycomb, and it can also be considered as an enhanced design on the existing common 3D re-entrant lattice structure (CRLS) by embedding a 3D Kagome truss into every cell of it. Analytical models were developed for predicting the Young’s modulus and Poisson’s ratio of the new structure and then verified by the numerical simulations and experiments. A comparison between the new structure and the existing 3D re-entrant lattice structures was carried out. The influences of the micro geometrical parameters on the macro mechanical properties were discussed to fully understand the elastic behavior of the new structure. It is shown that, the relation between the normalized Yong’s modulus, \({{\hat{E}} \mathord{\left/ {\vphantom {{\hat{E}} {E_{0} }}} \right. \kern-0pt} {E_{0} }}\) E ^ E ^ E 0 E 0 , and the relative density, \({{\rho^{*} } \mathord{\left/ {\vphantom {{\rho^{*} } {\rho_{0} }}} \right. \kern-0pt} {\rho_{0} }}\) ρ ρ ρ 0 ρ 0 of the 3D lattice structures follows a simple exponential function, i.e., \(\left( {{{\hat{E}} \mathord{\left/ {\vphantom {{\hat{E}} {E_{0} }}} \right. \kern-0pt} {E_{0} }}} \right) = C \cdot \left( {{{\rho^{*} } \mathord{\left/ {\vphantom {{\rho^{*} } {\rho_{0} }}} \right. \kern-0pt} {\rho_{0} }}} \right)^{m}\) E ^ E ^ E 0 E 0 = C · ρ ρ ρ 0 ρ 0 m . In the case of CRLS, m tends to 2, while m is close to 1 for the new structure, which reveals that the dominated deformation mode of the CRLS is changed by the embedded struts from bending to stretching. As a result, the new structure has larger specific stiffness with respect to CRLS. Compared to the two existing 3D embedded enhanced re-entrant lattice structures (single rib embedded re-entrant lattice, SRELS, and the spatial rhombic truss embedded lattice structure, SRTELS), the new 3D structure exhibits weaker anisotropy and stronger auxetic effect, which makes the new structure have better application advantages in some specific occasions. This work may provide a good guide for the development of the 3D auxetic lattcie structures with improved mechanical performance.