颗粒介质物质点法与离散元法的多尺度建模
|
摘要
颗粒介质是由大量离散颗粒构成的无序材料,在工业生产与自然界中广泛存在.在外界作用下,颗粒材料可以类似固体保持稳定,也可类似流体发生流动,且类固体和类流体之间可以自然转化,目前人们难以采用统一的连续本构进行描述.本文提出了物质点法(Material Point Method,MPM)与离散元法(Discrete Element Method,DEM)的多尺度建模框架,亦即宏观尺度采用适用于大变形问题的MPM,颗粒尺度则采用DEM描述每个颗粒运动,每个物质点的力学性质由该点处若干颗粒构成的代表性体积元的力学性质计算得到,宏观尺度MPM所得变形梯度作为边界条件施加到体积元中,基于DEM计算得到域内的平均柯西应力,反馈到MPM计算,以此实现跨尺度研究.以沙堆倒塌作为算例,验证了MPM/DEM多尺度建模在描述颗粒复杂力学行为的有效性,并对倒塌过程中,宏观应变等信息与内在接触力链网络的关联进行了讨论.MPM/DEM多尺度建模没有引入唯象本构,且适用于大变形问题,为颗粒介质的多力学状态研究提供了新的思路.
Granular materials are composed by discrete particles,which are often observed in geo-hazards,such as debris flows.It is difficult to establish unified constitutive relations to describe the multiple-state properties of granular materials,i.e.,solidand fluid-like states and in-between transitions.In this study,a hierarchical multi-scale modelling scheme is developed based on the concept of black box theme.The macroscopic behavior is modelled by using material point method(MPM),which is suitable for large deformation treatment,while the constitution relations at each material point are extracted from discrete element method(DEM) modelling.By using the MPM/DEM modelling,the collapse of a sand pile is simulated and compared with experiments.The correlations between macroscopic phenomenons and microscopic network of force chain are illustrated.This MPM/DEM multi-scale modelling does not need any constitutive relations,and facilitates effective cross-scale interpretation and understanding of granular flow behaviors.It provides a potential approach to study the multiple states and large deformations of granular materials,especially when the constitutive relations cannot be expressed explicitly.
Granular materials are composed by discrete particles,which are often observed in geo-hazards,such as debris flows.It is difficult to establish unified constitutive relations to describe the multiple-state properties of granular materials,i.e.,solidand fluid-like states and in-between transitions.In this study,a hierarchical multi-scale modelling scheme is developed based on the concept of black box theme.The macroscopic behavior is modelled by using material point method(MPM),which is suitable for large deformation treatment,while the constitution relations at each material point are extracted from discrete element method(DEM) modelling.By using the MPM/DEM modelling,the collapse of a sand pile is simulated and compared with experiments.The correlations between macroscopic phenomenons and microscopic network of force chain are illustrated.This MPM/DEM multi-scale modelling does not need any constitutive relations,and facilitates effective cross-scale interpretation and understanding of granular flow behaviors.It provides a potential approach to study the multiple states and large deformations of granular materials,especially when the constitutive relations cannot be expressed explicitly.
引文
1 Jaeger H M,Nagel S R,Behringer R P.Granular solids,liquids,and gases.Rev Mod Phys,1996,68:1259–1273
2 Wang W H.The nature and properties of amorphous matter(in Chinese).Prog Phys,2013,33:177–351[汪卫华.非晶态物质的本质和特性.物理学进展,2013,33:177–351]
3 Sun Q C,Wang G Q.Introduction to the Mechanics of Granular Materuals(in Chinese).Beijing:Science Press,2009[孙其诚,王光谦.颗粒物质力学导论.北京:科学出版社,2009]
4 Li X,Wan K.A bridging scale method for granular materials with discrete particle assembly-cosserat continuum modeling.Comput Geotech,2011,38:1052–1068
5 Li G X.Characteristics and development of Tsinghua elasto-plastic model for soil(in Chinese).Chin J Geotech Eng,2006,28:1–10[李广信.土的清华弹塑模型及其发展.岩土工程学报,2006,28:1–10]
6 Andrade J,Avila C,Hall S,et al.Multiscale modeling and characterization of granular matter:From grain kinematics to continuum mechanics.J Mech Phys Solids,2011,59:237–250
7 Li X,Yu H S.Particle-scale insight into deformation noncoaxiality of granular materials.Int J Geomech,2013,15:04014061
8 Guo N,Zhao J.A coupled fem/dem approach for hierarchical multiscale modelling of granular media.Int J Numer Methods Eng,2014,99:789 –818
9 Nguyen T,Combe G,Caillerie D,et al.Fem×dem modelling of cohesive granular materials:Numerical homogenisation and multi-scale simulations.Acta Geophys,2014,62:1109–1126
10 Wang Y,Lu Y,Ooi J Y.A numerical study of wall pressure and granular flow in a flat-bottomed silo.Powder Tech,2015,282:43–54
11 Zhang X,Krabbenhoft K,Pedroso D,et al.Particle finite element analysis of large deformation and granular flow problems.Comput Geotech,2013,54:133–142
12 Bui H H,Fukagawa R,Sako K,et al.Lagrangian meshfree particles method(sph)for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive model.Int J Numer Anal Methods Geomech,2008,32:1537–1570
13 Ma S,Zhang X,Qiu X.Comparison study of mpm and sph in modeling hypervelocity impact problems.Int J Impact Eng,2009,36:272–282
14 Bardenhagen S,Kober E.The generalized interpolation material point method.Comput Mod Eng Sci,2004,5:477–496
15 Campbell C S.Granular material flows—An overview.Powder Tech,2006,162:208–229
16 Kozicki J,DonzéF.Yade-open dem:An open-source software using a discrete element method to simulate granular material.Eng Comput,2009,26 :786–805
2 Wang W H.The nature and properties of amorphous matter(in Chinese).Prog Phys,2013,33:177–351[汪卫华.非晶态物质的本质和特性.物理学进展,2013,33:177–351]
3 Sun Q C,Wang G Q.Introduction to the Mechanics of Granular Materuals(in Chinese).Beijing:Science Press,2009[孙其诚,王光谦.颗粒物质力学导论.北京:科学出版社,2009]
4 Li X,Wan K.A bridging scale method for granular materials with discrete particle assembly-cosserat continuum modeling.Comput Geotech,2011,38:1052–1068
5 Li G X.Characteristics and development of Tsinghua elasto-plastic model for soil(in Chinese).Chin J Geotech Eng,2006,28:1–10[李广信.土的清华弹塑模型及其发展.岩土工程学报,2006,28:1–10]
6 Andrade J,Avila C,Hall S,et al.Multiscale modeling and characterization of granular matter:From grain kinematics to continuum mechanics.J Mech Phys Solids,2011,59:237–250
7 Li X,Yu H S.Particle-scale insight into deformation noncoaxiality of granular materials.Int J Geomech,2013,15:04014061
8 Guo N,Zhao J.A coupled fem/dem approach for hierarchical multiscale modelling of granular media.Int J Numer Methods Eng,2014,99:789 –818
9 Nguyen T,Combe G,Caillerie D,et al.Fem×dem modelling of cohesive granular materials:Numerical homogenisation and multi-scale simulations.Acta Geophys,2014,62:1109–1126
10 Wang Y,Lu Y,Ooi J Y.A numerical study of wall pressure and granular flow in a flat-bottomed silo.Powder Tech,2015,282:43–54
11 Zhang X,Krabbenhoft K,Pedroso D,et al.Particle finite element analysis of large deformation and granular flow problems.Comput Geotech,2013,54:133–142
12 Bui H H,Fukagawa R,Sako K,et al.Lagrangian meshfree particles method(sph)for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive model.Int J Numer Anal Methods Geomech,2008,32:1537–1570
13 Ma S,Zhang X,Qiu X.Comparison study of mpm and sph in modeling hypervelocity impact problems.Int J Impact Eng,2009,36:272–282
14 Bardenhagen S,Kober E.The generalized interpolation material point method.Comput Mod Eng Sci,2004,5:477–496
15 Campbell C S.Granular material flows—An overview.Powder Tech,2006,162:208–229
16 Kozicki J,DonzéF.Yade-open dem:An open-source software using a discrete element method to simulate granular material.Eng Comput,2009,26 :786–805