隐式梯度模型在结构三维损伤数值模拟中的应用
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摘要
本文简单总结了损伤力学产生的背景及其基本理论,介绍了几种混凝土的局部损伤模型和非局部损伤模型,并分析了这两类模型的不同点及应用前景。为了克服局部损伤模型在数值模拟中存在的网格敏感性与病态局部化问题,在推导非局部模型的基本公式和控制方程时考虑了材料的内部尺度值,并引入了高阶变形梯度项,推导出了隐式梯度模型的基本公式及其有限元离散的控制方程,并将其有效应用于有限元求解程序中。文章重点讨论了求解过程中插值形函数的选取原则,提出了含裂缝混凝土板裂尖应变场奇异性的处理方法,即用线性外插法求解裂尖应变场。编制了有限元程序,并用该程序对平面应力状态下含裂缝板件的损伤和受集中载荷简支梁的三维损伤进行了数值模拟。分析了上两类构件在三种网格下的载荷位移曲线、及损伤分布云图和材料的损伤演变曲线。结果表明,隐式梯度模型可以很好地模拟混凝土材料的三维损伤特性,并且其损伤分布和承载力峰值对于网格的细化不敏感,解决了网格依赖性和零能量损耗问题。
In this paper, the procreant background and basic theory of damage mechanics was summarized, several kinds of local damage model and nonlocal damage model of concrete were introduced, and their differential and applied foreground was analysed. The micro structure criterion was considered and the high-order distor- tion grads items was introduced when the basic formula and manipulative equation of nonlocal damage model was deducted so as to overcome mesh-dependence and sick localization in numerical simulation. The basic formula and manipulative equation of implicit gradient damage model were deducted, and were applied to finite element computation program. The defining principle of the interpolations functions was discussed emphatically in the computation process in this paper, the singularity for the strain field at the crack tip of concrete board with crack was studied,and the numerical extrapolated method was applied at the crack tip. The damage of concrete plate with crack of plane-stress and three-dimensional dam- age of three curved beems were simulated. The curve of load-displacement and nephogram of damage distributing with three mesh were gained, and the curve of damage evolvement was analysed. Numerical calculation show that the implicit gradient model can simulate commendably the speciality of damage for concrete,and its distributing of damage and carrying capacity is no sensitivity to mesh- diminished. The pathological mesh-dependence and zero energy consuming are overcome.
In this paper, the procreant background and basic theory of damage mechanics was summarized, several kinds of local damage model and nonlocal damage model of concrete were introduced, and their differential and applied foreground was analysed. The micro structure criterion was considered and the high-order distor- tion grads items was introduced when the basic formula and manipulative equation of nonlocal damage model was deducted so as to overcome mesh-dependence and sick localization in numerical simulation. The basic formula and manipulative equation of implicit gradient damage model were deducted, and were applied to finite element computation program. The defining principle of the interpolations functions was discussed emphatically in the computation process in this paper, the singularity for the strain field at the crack tip of concrete board with crack was studied,and the numerical extrapolated method was applied at the crack tip. The damage of concrete plate with crack of plane-stress and three-dimensional dam- age of three curved beems were simulated. The curve of load-displacement and nephogram of damage distributing with three mesh were gained, and the curve of damage evolvement was analysed. Numerical calculation show that the implicit gradient model can simulate commendably the speciality of damage for concrete,and its distributing of damage and carrying capacity is no sensitivity to mesh- diminished. The pathological mesh-dependence and zero energy consuming are overcome.
引文
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[24].李兆霞,Z.Mroz.应变率相关的粘塑性损伤本构模型.岩石,混凝土裂纹和强度,学术会议论文集,国防科技大学出版社,1993.
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[29].任青文,徐道远等.复杂条件下的高拱坝(300米级)建设中的应用基础研究,国家自然科学基金委员会,1997:1-53.
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[31].Noh.Sam-Yong,Kratzig,wilfried.B,Meskourid.konsiantin.Numerical simulation of service ability,damage evolution and failure of reinforced concrete shells. Computer and structures,v81,n8-1l, p843-857 May,2003.
[32].张强勇,朱维申,金亚兵.弹塑性损伤模型在某地下厂房中的应用[J],岩石力学与工程学报,1999.18( 6):654-657.
[33].Carmeliet J and Hens H.Probabilistic nonlocal damage model for continua with random field properties.J Engineering Mechanics, 1994,120(10):2013～2027.
[34].赵吉东,周维垣,刘元高,杨若琼.岩石类材料应变梯度损伤模型研究及应用[J].水利学报,2002,(7):70—74.
[35].赵吉东,周维垣,刘元高.基于应变梯度的损伤局部化研究及应用[J].力学学报,2002,34(3):445—452.
[36].赵扬锋,潘一山.岩石单轴压缩应变梯度损伤模型局部化带宽[J].辽宁工程技术大学学报,2006,25(3):355—357.
[37].王学滨.考虑应变梯度及刚度劣化的剪切带局部变形分析[J].工程力学,2006,23(10):101—106.
[38].燕秀发,戴耀.功能梯度材料裂纹高阶渐近场研究[J].机械强度,2006,28(4):593—597.
[39].Aifantis EC. On the role of gradient in the localization of deformation and fracture.Int J Engng Sci,1992,30:1279—1299.
[40].Roy A.B.Engelen,Marc G.D.Geers,Frank P.T.Baaijens.International Journal of Plasticity 19(2003)403-433.
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