具有负压缩性的铰接八面体结构的有限元分析
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摘要
为探究铰接八面体结构的线压缩性与模型几何参数之间的内在关联,对该三维结构进行了有限元分析。在保证其他几何尺寸不变的前提下,通过改变杆长比l_1/l_2和杆件夹角θ_1,建立了不同的有限元模型。具体讨论了杆长比和杆件夹角对该结构轴向线负压缩性(即NLC)大小和范围的影响。研究发现,通过合理地选择几何参数,该结构在3个轴线方向上均可存在线负压缩性,其中杆件夹角θ_1的大小决定了线压缩性的正负,杆长比l_1/l_2的大小则决定了负压缩性的大小和存在范围。
In order to investigate the inherent link between the linear compressibility properties and the geometrical parameters, the 3D hinging octahedron structure was analyzed by a finite element method.With constant geometry size, different finite element models were established by changing the rod length ratio of l_1/l_2 and angle θ_1 between the two rods. The effects of these two structure parameters on the magnitude as well as the range of negative linear compressibility(i.e. NLC) of this structure were analyzed and discussed. It is shown that through carefully choosing the geometry parameters, NLC can be exhibited in this model along the three-axis directions. More specifically, the sign of the linear compressibility is determined by the angle θ_1 while the magnitude and range of NLC are determined by the l_1/l_2 ratio.
In order to investigate the inherent link between the linear compressibility properties and the geometrical parameters, the 3D hinging octahedron structure was analyzed by a finite element method.With constant geometry size, different finite element models were established by changing the rod length ratio of l_1/l_2 and angle θ_1 between the two rods. The effects of these two structure parameters on the magnitude as well as the range of negative linear compressibility(i.e. NLC) of this structure were analyzed and discussed. It is shown that through carefully choosing the geometry parameters, NLC can be exhibited in this model along the three-axis directions. More specifically, the sign of the linear compressibility is determined by the angle θ_1 while the magnitude and range of NLC are determined by the l_1/l_2 ratio.
引文
[1]Morosin B,Schirber J E.Linear compressibilities and the pressure dependence of the atomic positional parameter of As[J].Solid State Communications,1972,10(3):249-251.
[2]Skelton E F,Feldman J L,Liu C Y,et al.Study of the pressure-induced phase transition in paratellurite(TeO2)[J].Physical Review B,1976,13(6):2605-2613.
[3]Mariathasan J W E,Finger L W,Hazen R M.Highpressure behavior of LaNbO4[J].Acta Crystallographica Section B:Structural Science,1985,41(3):179-184.
[4]Fortes A D,Suard E,Knight K S.Negative linear compressibility and massive anisotropic thermal expansion in methanol monohydrate[J].Science,2011,331(6018):742-746.
[5]Baughman R H,Stafstrom S,Cui C,et al.Materials with negative compressibility in one or more dimensions[J].Science,1998,279(5356):1522-1524.
[6]Grima J N,Attard D,Caruana-Gauci R,et al.Negative linear compressibility of hexagonal honeycombs and related systems[J].Scripta Materialia,2011,65(7):565-568.
[7]Barnes D L,Miller W,Evans K E,et al.Modelling negative linear compressibility in tetragonal beam structures[J].Mechanics of Materialia,2012,46:123-128.
[8]Grima J N,Caruana-Gauci R,Wojciechowski K W,et al.Smart hexagonal truss systems exhibiting negative compressibility through constrained angle stretching[J].Smart Materials and Structures,2013,22(8):84015.
[9]Grima J N,Attard D,Gatt R.Truss-type systems exhibiting negative compressibility[J].Physical Status Solidi,2008,245(11):2405-2414.
[10]Choi J B,Lakes R S.Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative Poisson's ratio[J].International Journal of Mechanical Science,1995,37(1):51-59.
[11]Choi J B,Lakes R S.Nonlinear analysis of the Poisson's ratio of negative Poisson's ratio foams[J].Journal of Composite Materials,1995,29(1):113-128.
[12]Lu Z X,Liu Q,Yang Z Y.Predictions of Young's modulus and negative Poisson's atio of auxetic foams[J].Physica Status Solidi B,2011,248:167-174.
[13]Li K,Gao X L,Roy A K.Micromechanics model for three-dimensional open-cell foams using a tetrakaidecahedral unit cell and Castigliano's second theorem[J].Composites Science and Technology,2003,63(12):1769-1781.
[14]Grima J N,Caruana-Gauci R,Attard D,et al.Threedimensional cellular structures with negative Poisson's ratio and negative compressibility properties[J].Proceedings of the Royal Society A:Mathematical Physical and Engineering Sciences,2012,468(2146):3121-3138.
[15]Xie Y M,Yang X Y,Shen J H et.al.Designing orthotropic materials for negative or zero compressibility[J].International Journal of Solids and Structures,2014,51(23/24):4038-4051.
[16]Zhou X Q,Zhang L,Zhang H,et al.3D cellular models with negative compressibility through the wine-rack-type mechanism:3D cellular models with negative compressibility[J].Physica Status Solidi,2016,253(10):1977-1993.
[17]Masters I G,Evans K E.Models for the elastic deformation of honeycombs[J].Composite Structures,1996,35:403-422.
[2]Skelton E F,Feldman J L,Liu C Y,et al.Study of the pressure-induced phase transition in paratellurite(TeO2)[J].Physical Review B,1976,13(6):2605-2613.
[3]Mariathasan J W E,Finger L W,Hazen R M.Highpressure behavior of LaNbO4[J].Acta Crystallographica Section B:Structural Science,1985,41(3):179-184.
[4]Fortes A D,Suard E,Knight K S.Negative linear compressibility and massive anisotropic thermal expansion in methanol monohydrate[J].Science,2011,331(6018):742-746.
[5]Baughman R H,Stafstrom S,Cui C,et al.Materials with negative compressibility in one or more dimensions[J].Science,1998,279(5356):1522-1524.
[6]Grima J N,Attard D,Caruana-Gauci R,et al.Negative linear compressibility of hexagonal honeycombs and related systems[J].Scripta Materialia,2011,65(7):565-568.
[7]Barnes D L,Miller W,Evans K E,et al.Modelling negative linear compressibility in tetragonal beam structures[J].Mechanics of Materialia,2012,46:123-128.
[8]Grima J N,Caruana-Gauci R,Wojciechowski K W,et al.Smart hexagonal truss systems exhibiting negative compressibility through constrained angle stretching[J].Smart Materials and Structures,2013,22(8):84015.
[9]Grima J N,Attard D,Gatt R.Truss-type systems exhibiting negative compressibility[J].Physical Status Solidi,2008,245(11):2405-2414.
[10]Choi J B,Lakes R S.Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative Poisson's ratio[J].International Journal of Mechanical Science,1995,37(1):51-59.
[11]Choi J B,Lakes R S.Nonlinear analysis of the Poisson's ratio of negative Poisson's ratio foams[J].Journal of Composite Materials,1995,29(1):113-128.
[12]Lu Z X,Liu Q,Yang Z Y.Predictions of Young's modulus and negative Poisson's atio of auxetic foams[J].Physica Status Solidi B,2011,248:167-174.
[13]Li K,Gao X L,Roy A K.Micromechanics model for three-dimensional open-cell foams using a tetrakaidecahedral unit cell and Castigliano's second theorem[J].Composites Science and Technology,2003,63(12):1769-1781.
[14]Grima J N,Caruana-Gauci R,Attard D,et al.Threedimensional cellular structures with negative Poisson's ratio and negative compressibility properties[J].Proceedings of the Royal Society A:Mathematical Physical and Engineering Sciences,2012,468(2146):3121-3138.
[15]Xie Y M,Yang X Y,Shen J H et.al.Designing orthotropic materials for negative or zero compressibility[J].International Journal of Solids and Structures,2014,51(23/24):4038-4051.
[16]Zhou X Q,Zhang L,Zhang H,et al.3D cellular models with negative compressibility through the wine-rack-type mechanism:3D cellular models with negative compressibility[J].Physica Status Solidi,2016,253(10):1977-1993.
[17]Masters I G,Evans K E.Models for the elastic deformation of honeycombs[J].Composite Structures,1996,35:403-422.