Parametric Variational Principle Based Elastic-Plastic Analysis of Heterogeneous Materials With Voronoi Finite Element Method
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摘要: 在非均质材料的有限元数值模拟中,采用了Voronoi单元(VCFEM)以克服经典位移元的局限性.基于参数变分原理和二次规划法进行了Voronoi单元的二维弹塑性分析A·D2推导了有限元列式并形成最终的二次规划求解模型.研究了非均质材料微观夹杂对整体力学性能的影响.数值算例证明了该方法的正确和可行性.Abstract: The Voronoi cell finite element method(VCFEM) is adopted to overcome the limitations of the classic displacement based finite element method in numerical simulation of heterogeneous materials.The parametric variational principle and quadratic programming method were developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems.Finite element formulations were derived and a standard quadratic programming model was deduced from the elastic-plastic equations.Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail.Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.
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[1] Brockenbrough J R, Suresh S, Wienecke H A. Deformation of metal-matrix composites with continuous fibers: geometrical effects of fiber distribution and shape[J].Acta Metall Mater,1991,39(5):735—752. doi: 10.1016/0956-7151(91)90274-5 [2] Christman T,Needleman A, Suresh S. An experimental and numerical study of deformation in metal-ceramic composites[J].Acta Metall Mater,1989,37(11):3029—3050. doi: 10.1016/0001-6160(89)90339-8 [3] Hashin Z,Strikman S.A variational approach to the theory of the elastic behavior of multiphase materials[J].J Mech Phys Solids,1963,11(2):127—140. doi: 10.1016/0022-5096(63)90060-7 [4] Chen H S, Acrivos A. The effective elastic moduli of composite materials containing spherical inclusions at non-dilute concentrations[J].Internat J Solids and Structures,1978,14(3):349—364. doi: 10.1016/0020-7683(78)90017-3 [5] Hill R. A self consistent mechanics of composite materials[J].J Mech Phys Solids,1965,13(4):213—222. doi: 10.1016/0022-5096(65)90010-4 [6] Hori M,Nemat-Nasser S. Double inclusion model and overall moduli of multiphase composites[J].J Mech Phys Solids,1993,14(2):189—206. [7] Bao G, Hutchinson J W,McMeeking R M.Plastic reinforcement of ductile matrices against plastic flow and creep[J].Acta Metall Mater,1991,39(5):1871—1882. doi: 10.1016/0956-7151(91)90156-U [8] Ghosh S, Mukhopadhyay S N. A material based finite elemtent analysis of heterogeneous media involving Dirichlet tessellations[J].Comput Methods Appl Mech Engrg,1993,104(3/4):211—247. doi: 10.1016/0045-7825(93)90198-7 [9] Pian T H H. Derivation of element stiffness matrices by assumed stress distribution[J].AAIA J,1964,2(5):1333—1336. doi: 10.2514/3.2546 [10] Zhang J,Katsube N.Problems related to application of eigenstrains in a finite element analysis[J].Internat J Numer Methods Engrg,1994,37(18):3185—3193. doi: 10.1002/nme.1620371811 [11] Zhang J, Katsube N. A hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions[J].Internat J Numer Methods Engrg,1995,38(10):1635—1653. doi: 10.1002/nme.1620381004 [12] Ghosh S, Moorthy S.Elastic-plastic analysis of arbitrary heterogeneous materials with the Voronoi cell finite element method[J].Comput Methods Appl Mech Engrg,1995,121(1/4):373—409. doi: 10.1016/0045-7825(94)00687-I [13] Ghosh S Lee K, Moorthy S. Multiple scale analysis of heterogeneous elastic structures using homogenization theory and Voronoi cell finite element method[J].Internat J Solids and Structures,1995,32(1):27—62. doi: 10.1016/0020-7683(94)00097-G [14] Grujicic M, Zhang Y.Determination of effective elastic properties of functionally graded materials using Voronoi cell finite element method[J].Materials Science and Engineering,Ser A,1998,251(1):64—76. doi: 10.1016/S0921-5093(98)00647-9 [15] Lee K, Ghosh S.A microstructure based numerical method for constitutive modeling of composite and porous materials[J].Materials Science and Engineering,Ser A,1999,272(1):120—133. doi: 10.1016/S0921-5093(99)00475-X [16] Raghavan P,Li S,Ghosh S. Two scale response and damage modeling of composite materials[J].Finite Elements in Analysis and Design,2004,40(12):1619—1640. doi: 10.1016/j.finel.2003.11.003 [17] 钟万勰.岩土力学中的参变量最小余能原理[J].力学学报,1986,18(3):253—258. [18] 钟万勰,张洪武,吴承伟.参变量变分原理及其在工程中的应用[M].北京:科学技术出版社,1997. [19] Zhang H W, Xu W L, Di S L,et al.Quadratic programming method in numerical simulation of metal forming process[J].Comput Methods Appl Mech Engrg,2002, 191(49):5555—5578. doi: 10.1016/S0045-7825(02)00462-0 [20] Zhang H W,Zhang X W,Chen J S. A new algorithm for numerical solution of dynamic elastic-plastic hardening and softening problems[J].Computers and Structures,2003,81(17):1739—1749. doi: 10.1016/S0045-7949(03)00167-6 [21] Zhang H W, Schrefler B A. Gradient-dependent plasticity model and dynamic strain localization analysis of saturated and partially saturated porous media: one dimensional model[J].European Journal of Solid Mechanics A/Solids,2000,19(3):503—524. doi: 10.1016/S0997-7538(00)00177-7
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