二维多尺度颗粒材料受压性能数值模拟
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摘要
颗粒材料的宏观力学行为是微观单个颗粒之间相互作用的结果。本文采用多尺度研究方法对已有试验进行了数值模拟,即在微观尺度下,采用离散元方法(DEM)对代表性结构单元(Representative Element Volume(REV))进行建模计算,在宏观尺度下采用有限单元法(FEM)进行求解。对FEM模型中高斯点处REV施加某一给定加载历史,采用均质计算方法获得REV全局应力张量,通过该应力张量推导FEM在每个高斯点的刚度矩阵,从而推导颗粒材料宏观数值本构响应。本文同时考虑了孔隙率,加载速度对压缩效率的影响。
On the macro-level,the behavior of granular materials is the consequence of the interactions of individual grains at the micro scale. A two-scale approach of computational homogenization is considered. At the micro scale,we consider granular structure REV( Representative Element Volume) modeled by the Discrete Element Method( DEM). On the macro scale,the problem is solved by Finite Element Method( FEM). The upscaling technique is that using the response of REV at each Gauss point of the FEM's formulation to derive the constitutive response through the global stress and strain tensor of the REV. The porosity and velocity of loading are both taken into account.
On the macro-level,the behavior of granular materials is the consequence of the interactions of individual grains at the micro scale. A two-scale approach of computational homogenization is considered. At the micro scale,we consider granular structure REV( Representative Element Volume) modeled by the Discrete Element Method( DEM). On the macro scale,the problem is solved by Finite Element Method( FEM). The upscaling technique is that using the response of REV at each Gauss point of the FEM's formulation to derive the constitutive response through the global stress and strain tensor of the REV. The porosity and velocity of loading are both taken into account.
引文
[1]Yu-Ching Wu.Automatic adaptive mesh upgrade schemes of the step-by-step incremental simulation for quasi linear viscoplastic granular materials[J].Computer Methods in Applied Mechanics and Engineering,2008,197:1 479-1 494.
[2]Y.C.Wu,E.G.Thompson,P.R.Heyliger,et al.The compaction of blended aggregates of non-spherical linear viscous particles[J].Computer Methods Applied Mechanics and Engineering,2004,193:3 871-3 890.
[3]周健,池永.砂土力学性质的细观模拟[J].岩土力学,2003,24(6):901-906.(Zhou Jian,Chi Yong.Simulation of sand mechanical properties[J].Rock and Solid Mechanics,2003,24(6):901-906.(in Chinese))
[4]孙其诚,金峰,王光谦,等.二维颗粒体系单轴压缩形成的力链结构[J].物理学报,2010,59(1):32-36.(Sun Qicheng,Jin Feng,Wang Guangqian,et al.Force chain structure formed from Two-dimensional granular system under uniaxial compression[J].Acta Physica Sinica,2010,59(1):32-36.(in Chinese))
[5]MichaNitka,Gaёl Combe,C Dascalu,et al.Twoscale modeling of granular materials:a DEM-FEM approach[J].Granular Matter,2011,13:277-281.
[6]Bagi K.Stress and strain in granular assemblies[J].Mechanics of Materials,1996,Vol.22:165-177.
[7]Erik G.Thompson.An Introduction To The Finite Element Method.John Wiley&Sons.Inc,2005.
[8]A.M.Cuitino,M.C.Alvarez,M.J.Roddy et al.,Experimental characterization of the behavior of granular visco-plastic and visco-elastic solids during compaction[J].Journal of Materials Science:2001,36:5 487-5 495.
[9]周健,池毓蔚,池永,等.砂土双轴试验的颗粒流模拟[J].岩土工程学报,2000,22(6):701-704(Zhou Jian,Chi Yuwei,Chi Yong,et al.Particle flow simulation of biaxial compression test[J].Chinese Journal of Geotechnical Engineering,2000,22(6):701-704.(in Chinese))
[10]Cundall PA.Particle flow code in two dimension user’s guide V4.0[M].Minnesota:Itasca Consulting Group.Inc,1999.
[2]Y.C.Wu,E.G.Thompson,P.R.Heyliger,et al.The compaction of blended aggregates of non-spherical linear viscous particles[J].Computer Methods Applied Mechanics and Engineering,2004,193:3 871-3 890.
[3]周健,池永.砂土力学性质的细观模拟[J].岩土力学,2003,24(6):901-906.(Zhou Jian,Chi Yong.Simulation of sand mechanical properties[J].Rock and Solid Mechanics,2003,24(6):901-906.(in Chinese))
[4]孙其诚,金峰,王光谦,等.二维颗粒体系单轴压缩形成的力链结构[J].物理学报,2010,59(1):32-36.(Sun Qicheng,Jin Feng,Wang Guangqian,et al.Force chain structure formed from Two-dimensional granular system under uniaxial compression[J].Acta Physica Sinica,2010,59(1):32-36.(in Chinese))
[5]MichaNitka,Gaёl Combe,C Dascalu,et al.Twoscale modeling of granular materials:a DEM-FEM approach[J].Granular Matter,2011,13:277-281.
[6]Bagi K.Stress and strain in granular assemblies[J].Mechanics of Materials,1996,Vol.22:165-177.
[7]Erik G.Thompson.An Introduction To The Finite Element Method.John Wiley&Sons.Inc,2005.
[8]A.M.Cuitino,M.C.Alvarez,M.J.Roddy et al.,Experimental characterization of the behavior of granular visco-plastic and visco-elastic solids during compaction[J].Journal of Materials Science:2001,36:5 487-5 495.
[9]周健,池毓蔚,池永,等.砂土双轴试验的颗粒流模拟[J].岩土工程学报,2000,22(6):701-704(Zhou Jian,Chi Yuwei,Chi Yong,et al.Particle flow simulation of biaxial compression test[J].Chinese Journal of Geotechnical Engineering,2000,22(6):701-704.(in Chinese))
[10]Cundall PA.Particle flow code in two dimension user’s guide V4.0[M].Minnesota:Itasca Consulting Group.Inc,1999.