基于介观力学信息的颗粒材料损伤--愈合与塑性宏观表征

王增会; 李锡夔

doi:10.6052/0459-1879-17-362

基于介观力学信息的颗粒材料损伤--愈合与塑性宏观表征

大连理工大学工业装备结构分析国家重点实验室,大连 116024

基金项目: 国家自然科学基金资助项目(11372066).

详细信息

作者简介:
null

作者简介：李锡夔，教授，主要研究方向：计算力学，颗粒材料多尺度力学. E-mail: xikuili@dlut.edu.cn

中图分类号: O345;
计量
- 文章访问数: 01230
- HTML全文浏览量: 0171
- PDF下载量: 0316
出版历程
- 收稿日期: 2017-11-04
- 刊出日期: 2018-03-17

MESO-MECHANICALLY INFORMED MACROSCOPIC CHARACTERIZATION OF DAMAGE-HEALING-PLASTICITY FOR GRANULAR MATERIALS

The State Key Laboratory of Structure Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

摘要

摘要: 本文在二阶计算均匀化框架下提出了颗粒材料损伤--愈合与塑性的多尺度表征方法. 颗粒材料结构在宏观尺度模型化为梯度Cosserat连续体,在其有限元网格的每个积分点处定义具有离散颗粒介观结构的表征元. 建立了表征元离散颗粒系统的非线性增量本构关系. 表征元周边介质作用于表征元边界颗粒的增量力与增量力偶矩以表征元边界颗粒的增量线位移与增量转动角位移、当前变形状态下表征元离散介观结构弹性刚度、以及凝聚到表征元边界颗粒的增量耗散摩擦力表示. 基于平均场理论与Hill定理,导出了基于介观力学信息的梯度Cosserat连续体增量非线性本构关系. 在等温热动力学框架下定义了表征颗粒材料各向异性损伤--愈合和塑性的损伤、愈合张量因子与综合损伤、愈合效应的净损伤张量因子和塑性应变. 此外,定义了损伤和塑性耗散能密度与愈合能密度,以定量比较材料损伤、愈合、塑性对材料失效的效应. 应变局部化数值例题结果显示了所建议的颗粒材料损伤--愈合--塑性表征方法的有效性.
- 颗粒材料 /
- 梯度加强Cosserat连续体 /
- 离散颗粒集合体 /
- 二阶计算均匀化 /
- 各向损伤--愈合与塑性表征 /
- 热动力学
Abstract: The multiscale characterization of coupled damage-healing and plasticity for granular materials is presented in the frame of second-order computation homogenization. The structure composed of granular materials is modeled as Cosserat continuum at the macroscale. The representation volume element (RVE) possessing the meso-structure of discrete particle assembly is assigned at each of the integration points of the finite element mesh generated in the macroscopic continuum. The incremental non-linear constitutive relation for the discrete particle assembly of RVE is established. The incremental forces and couple moments applied to the peripheral particles on the boundary of the RVE from the medium outside the RVE are expressed in terms of the incremental translational and rotational displacements of peripheral particles of the RVE, the elastic stiffness of the current deformed meso-structural RVE, and the incremental dissipative frictional forces condensed to the peripheral particles of the RVE. Based on the average field theory and the Hill’s lemma, meso-mechanically informed macroscopic incremental nonlinear constitutive relation is derived for the gradient-enhanced Cosserat continuum. The tensorial damage, healing factors, and the tensorial net damage factor combining the effects of both the damage and the healing and the plastic strain to characterize anisotropic damage-healing and plasticity of granular materials are defined in the isothermal thermodynamic framework. In addition, densities of damage and plastic dissipative energies, the density of healing energy are defined so that the damage, the healing and the plastic effects on the failure of granular material are quantitatively comparable. The results of the example problem of strain localization demonstrate validity of the proposed method for characterizing the damage-healing-plasticity occurring in granular materials.

HTML全文

参考文献(1)

[1]	Alonso-marroquin F. Static equation of the Cosserat continuum derived from intra-granular stress. Granular Matter, 2011, 13(3): 189-196
[2]	Chang CS, Kuhn MR.On virtual work and stress in granular media.International Journal of Solids and Structures, 2005, 42(13): 3773-3793
[3]	D’Addetta GA, Ramm E. A particle center based homogenization strategy for granular assemblies.Engineering Computation, 2004, 21(2-3-4): 360-383
[4]	Li XK Liu QP, Zhang JB. A micro-macro homogenization approach for discrete particle assembly Cosserate continuum modeling of granular materials.International Journal of Solids and Structures, 2010, 47(2): 291-303
[5]	Ehlers W, Ramm E, Diebels S, et al.From particle ensembles to Cosserat continua: Homogenization of contact forces towards stresses and couple stresses.International Journal of Solids and Structures, 2003, 40(24): 6681-6702
[6]	Kruyt NP.Statics and kinematics of discrete Cosserat-type granular materials. International Journal of Solids and Structures, 2003, 40(3): 511-534
[7]	Pasternak E, Muhlhaus HB.Generalised homogenisation procedures for granular materials.Journal of Engineering Mathematics, 2005, 52(1-3): 199-229
[8]	Qu J, Cherkaoui M.Fundamentals of Micromechanics of Solids. New Jersey: Wiley, 2006
[9]	Li XK, Liu QP.A version of Hill’s lemma for Cosserat continuum.Acta Mechanica Sinica, 2009, 25: 499-506
[10]	Li XK, Zhang JB, Zhang X.Micro-macro homogenization of gradient-enhanced Cosserat media.European Journal of Mechanics A, 2011, 30(3): 362-372
[11]	Li XK, Zhang X, Zhang JB.A generalized Hill’s lemma and micromechanically based macroscopic constitutive model for heterogeneous granular materials.Computer Methods in Applied Mechanics and Engineering, 2010, 199(49-52): 3137-3152
[12]	Li XK, Liang YB, Quan QL, et al.A mixed finite element procedure of gradient Cosserat continuum for second-order computational homogenization of granular materials.Computational Mechanics, 2014, 54(5): 1331-1356
[13]	Kachanov L.Time rupture under creep conditions.Izvestiya Akademii Nauk SSSR, Otdelenie Tekhnicheskikh Nauk, 1958 8(8): 26-31
[14]	Lemaitre J, Chaboche JL.Mechanics of Solid Materials. Cambridge: Cambridge University Press, 1990
[15]	唐炳涛. 基于连续体损伤理论的硼钢高温成形极限确定法. 力学学报, 2016, 48(1): 146-153
[15]	(Tang Bingtao.Prediction of forming limit of boron steel at elevated temperatrue based on CDM theory.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 146-153 (in Chinese))
[16]	Chaboche JL.Continuum damage mechanics: Part I: General concept, Part II damage growth, crack initiation and crack growth.Journal of Applied Mechanics, 1988, 55(3): 59-71
[17]	Chow CL, Wang J.An anisotropic theory of elasticity for continuum damage mechanics.International Journal of Fracture, 1987, 33(1): 3-16
[18]	Ju JW.On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects.International Journal of Solids and Structures, 1989, 25(7): 803-833
[19]	Simo JC, Ju JW.Strain-based and stress-based continuum damage models, part I: Formulation.International Journal of Solids and Structures, 1987, 23: 821-840
[20]	Ladeveze P, LeDantec E. Damage modelling of the elementary ply for laminated composites.Composites Science and Technology, 1992, 43(3): 257-267
[21]	Darabi MK, Al-Rub RKA, Little DN.A continuum damage mechanics framework for modeling micro-damage healing.International Journal of Solids and Structures, 2012, 49(3-4): 492-513
[22]	Herbst O, Luding S.Modeling particulate self-healing materials and application to uni-axial compression.International Journal of Fracture, 2008, 154(1-2): 87-103
[23]	Mergheim J., Steinmann P.Phenomenological modelling of self-healing polymers based on integrated healing agents.Computational Mechanics, 2013, 52(3): 681-692
[24]	Aliko-Benteza A, Doblaré M, Sanz-Herrera JA. Chemical-diffusive modeling of the self-healing behavior in concrete. International Journal of Solid and Structures, 2015, 69-70: 392-402
[25]	陈洁,刘剑兴,姜德义等. 围压作用下岩盐应变与损伤恢复试验研究. 岩土力学,2016, 37(1): 105-112
[25]	(Chen Jie, Liu Jianxing, Jiang Deyi, et al.An experimental study of strain and damage recovery of salt rock under confining pressures. Rock and Soil Mechanics, 2016, 37(1): 105-112 (in Chinese))
[26]	Barbero EJ, Greco F, Lonetti P.Continuum damage-healing mechanics with application to self-healing composites.International Journal of Damage Mechanics, 2005, 14(1): 51-81
[27]	Voyiadjis GZ, Shojaei A, Li G.A thermodynamic consistent damage and healing model for self healing materials.International Journal of Plasticity, 2011, 27(7): 1025-1044
[28]	Voyiadjis GZ, Shojaei A, Li GQ, et al.Continuum damage-healing mechanics with introduction to new healing variables. International Journal of Damage Mechanics, 2012, 21(3): 391-419
[29]	Voyiadjis GZ and Kattan PI. Healing and super healing in continuum damage mechanics. International Journal of Damage Mechanics, 2014, 23(2): 245-260
[30]	张浪平,尹祥础,梁乃刚. 地震条件下损伤--愈合模型的初步研究. 岩土力学与工程学报,2008, 27(2): 3956-3962
[30]	(Zhang Langping, Yin Xiangchu, Liang Naigang.Preliminary study on damage-healing model under earthquake. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(2): 3956-3962 (in Chinese))
[31]	Ju JW, Yuan KY, Kuo AW.Novel strain energy coupled elastoplastic damage and healing models for geomaterials-Part I: Formulations.International Journal of Damage Mechanics, 2012 21(4): 525-549
[32]	Ju JW, Yuan KY.New strain energy based coupled elastoplastic two-parameter damage and healing models for earth moving processes.International Journal of Damage Mechanics, 2012, 21(7): 989-1019
[33]	屈家旺,刘泉生,何军等. 泥岩弹塑性损伤--愈合模型研究. 岩土力学与工程学报, 2014, 33(1): 3192-3197
[33]	(Qu Jiangwang, Liu Quansheng, He Jun, et al.Study of elastoplastic damage-healing model for argillite,Chinese Journal of Rock Mechanics and Engineering, 2014, 33(1): 3192-3197 (in Chinese))
[34]	Li XK, Duxbury PD, Lyons L.Coupled creep-elastoplastic-damage analysis for isotropic and anisotropic nonlinear materials.International Journal of Solids and Structure, 1994, 31(9), 1181-1206
[35]	Li XK, Du YY, Duan QL.Micromechanically informed constitutive model and anisotropic damage characterization of Cosserat continuumfor granular materials.International Journal of Damage Mechanics, 2013, 22(5), 643-682
[36]	付云伟,倪新华,刘协权等. 颗粒缺陷相互作用下复合材料的细观损伤模型. 力学学报, 2016, 48(6): 1334-1342
[36]	(Fu Yunwei, Ni Xinhua, Liu Xiequan, et al.Micro-damage model of composite materials with particle and defect interaction.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(6): 1334-1342 (in Chinese))
[37]	郭洪宝, 王波, 贾普荣等. 平纹编织陶瓷基复合材料面内剪切细观损伤行为研究. 力学学报, 2016, 48(2): 361-368
[37]	(Guo Hongbao, Wang Bo, Jia Purong, et al.Mesoscopic damage behaviors of plain woven ceramic composite under in-plane shear loading.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(2): 361-368 (in Chinese))
[38]	Li XK, Du YY, Duan QL, et al.Thermodynamic framework for damage-healing-plasticity of granular materials and net damage variable,International Journal of Damage Mechanics, 2016, 25(2): 153-177
[39]	Li XK, Wang ZH, Liang, YB et al. Mixed FEM-crushable DEM nested scheme in second-order computational homogenization for granular materials.International Journal of Geomechanics, 2016, 16(5): C4016004