含能材料变泊松比粘弹性本构及其数值实现方法
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摘要
为研究含能材料变泊松比粘弹力学行为,基于热流变简单材料假设,建立了一种采用时间相关泊松比的三维热粘弹性本构方程;利用积分算法对该本构进行数值离散,给出了相应的应力更新方法;基于Abaqus软件UMAT接口技术编制了相应材料子程序,完成了算例分析。结果表明,数值解与对应解析解吻合良好,并通过了合理性算例验证,分析方法及算法程序有效,可为后续三维装药精细结构完整性分析提供支持;粘弹材料泊松比具有时间相关性,其较小变化对计算结果影响显著,尤其是在短时加载或状态转变过程。
To study the viscoelastic behavior of energetic materials with variable Poisson's ratio,based on the thermorheologically simple material hypothesis,a three-dimensional thermo-viscoelastic constitutive model with time-dependent Poisson 's ratio was built,and it was numerically studied and discretized into incremental form by integration algorithms,the corresponding stress-updating method was presented,then the Abaqus-based material subroutine was built using Fortran code and applied into several examples.The results show that numerical solutions agree well with corresponding analytical solutions with high accuracy,the soundness verification is passed,the designed analysis method and code is effective and would be applied to structural analysis for energetic material media such as practical explosive or propellant grain; The Poisson's ratio of viscoelastic materials is time-dependent,and its small change has a significant impact on the calculation results,especially in the short-term loading or state transition region.
To study the viscoelastic behavior of energetic materials with variable Poisson's ratio,based on the thermorheologically simple material hypothesis,a three-dimensional thermo-viscoelastic constitutive model with time-dependent Poisson 's ratio was built,and it was numerically studied and discretized into incremental form by integration algorithms,the corresponding stress-updating method was presented,then the Abaqus-based material subroutine was built using Fortran code and applied into several examples.The results show that numerical solutions agree well with corresponding analytical solutions with high accuracy,the soundness verification is passed,the designed analysis method and code is effective and would be applied to structural analysis for energetic material media such as practical explosive or propellant grain; The Poisson's ratio of viscoelastic materials is time-dependent,and its small change has a significant impact on the calculation results,especially in the short-term loading or state transition region.
引文
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[15]Hilton H H.Clarifications of certain ambiguities and failings of Poisson's ratios in linear viscoelasticity[J].Journal of E-lasticity,2011,104(1):5155-5161.
[16]张海联,周建平.固体推进剂药柱的近似不可压缩粘弹性增量有限元法[J].固体火箭技术,2001,24(2):36-40.ZHANG Hailian,ZHOU Jianping.Near-incompressible viscoelastic incremental finite element analysis of solid propellant grains[J].Journal of Solid Rocket Technology,2001,24(2):36-40.
[17]孟红磊,鞠玉涛.含损伤非线性粘弹性本构模型及其数值仿真应用[J].固体火箭技术,2012,35(6):764-768.MENG Honglei,JU Yutao.Nonlinear viscoelastic equation with cumulative damage and its application on numerical simulation[J].Journal of Solid Rocket Technology,2012,35(6):764-768.
[18]Zienkiewicz O C,Taylor R L.The finite element method for solid and structural mechanics(Sixth edition)[M].Oxford:Elsevier Butterworth-Heinemann publications,2005.
[19]王元有.推进剂药柱在内压力载荷下的应力、应变的粘弹性分析[J].兵工学报,1983,4(3):20-33.WANG Yuanyou.Viscoelastic analysis of stresses and strains in solid propellant grains under pressure loadings[J].Acta Armamentarii,1983,4(3):20-33.
[2]Jung G D,Youn S K,Kim B K.A three-dimensional nonlinear viscoelastic constitutive model of solid propellant[J].International Journal of Solids and Structures,2000,37(34):4715-4732.
[3]Ho S Y.High strain-rate constitutive models for solid rocket propellants[J].Journal of Propulsion and Power,2002,18(5):1106-1111.
[4]Hinterhoelzl R M,Schapery R A.FEM implementation of a three-dimensional viscoelastic constitutive model for particulate composites with damage growth[J].Mechanics of TimeDependent Materials,2004,8(1):65-94.
[5]Xu F,Aravas N,Sofronis P.Constitutive modeling of solid propellant materials with evolving microstructural damage[J].Journal of the Mechanics and Physics of Solids,2008,56(5):2050-2073.
[6]中国航天标准化研究所.复合固体推进剂泊松比试验方法:QJ 3228-2005[S].2006.China Institute of Aerospace Standardization.Poisson's ratio test method for composite solid propellants:QJ 3228-2005[S].2006.
[7]国防科学技术委员会.火药试验方法.方法414.4泊松比引伸计法:GJB 770B-2005[S].2006.National Defense Science and Technology Commission.Test methods for explosives.Method 414.4:GJB 770B-2005[S].2006.
[8]Christensen R M.Theory of viscoelasticity:An introduction[M].New York:Academia Press,1982.
[9]赵伯华.粘弹性泊松比与动态复数泊松比的研究[J].推进技术,1995,16(3):1-7.ZHAO Bohua.An investigation on viscoelastic Poisson's ratio and dynamic complex Poisson's ratio[J].Journal of Propulsion Technology,1995,16(3):1-7.
[10]Farruggia F,Perre P.Microscopic tensile test in the transverse plane of earlywood and latewood parts of spruce[J].Wood Science and Technology,2000,34(2):65-82.
[11]Qi H Y,Zhou L Z,Yang X G.Measurement of Young's modulus and Poisson's ratio of thermal barrier coatings[J].Chinese Journal of Aeronautics,2005,18(2):180-184.
[12]Lakes R S.The time-dependent Poisson's ratio of viscoelastic materials can increase or decrease[J].Cellular Polymers,1992,11(1):466-469.
[13]Tschoegl N W,Knauss W G,Emri I.Poisson's ratio in viscoelasticity:A critical review[J].Mechanics of time-dependent materials,2002,6(1):3-51.
[14]Michaeli M,Shtark A,Grosbein H,et al.Analytical,experimental and computational viscoelastic material characterizations absent Poisson's ratios[R].AIAA 2011-1809.
[15]Hilton H H.Clarifications of certain ambiguities and failings of Poisson's ratios in linear viscoelasticity[J].Journal of E-lasticity,2011,104(1):5155-5161.
[16]张海联,周建平.固体推进剂药柱的近似不可压缩粘弹性增量有限元法[J].固体火箭技术,2001,24(2):36-40.ZHANG Hailian,ZHOU Jianping.Near-incompressible viscoelastic incremental finite element analysis of solid propellant grains[J].Journal of Solid Rocket Technology,2001,24(2):36-40.
[17]孟红磊,鞠玉涛.含损伤非线性粘弹性本构模型及其数值仿真应用[J].固体火箭技术,2012,35(6):764-768.MENG Honglei,JU Yutao.Nonlinear viscoelastic equation with cumulative damage and its application on numerical simulation[J].Journal of Solid Rocket Technology,2012,35(6):764-768.
[18]Zienkiewicz O C,Taylor R L.The finite element method for solid and structural mechanics(Sixth edition)[M].Oxford:Elsevier Butterworth-Heinemann publications,2005.
[19]王元有.推进剂药柱在内压力载荷下的应力、应变的粘弹性分析[J].兵工学报,1983,4(3):20-33.WANG Yuanyou.Viscoelastic analysis of stresses and strains in solid propellant grains under pressure loadings[J].Acta Armamentarii,1983,4(3):20-33.
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