双稳态复合材料层合结构的黏弹性模型
Viscoelastic model of bistable composite laminated structures

为探明双稳态复合材料层合结构在复杂环境条件下的应用，对双稳态复合材料层合结构的黏弹性行为进行了研究。首先，将纤维简化为弹性材料，考虑基底材料的黏弹性行为。然后，根据纤维和基底的材料属性，通过理论分析得到了双稳态复合材料层合结构的黏弹性材料属性；根据经典层合板理论、最小应变能原理和Maxwell黏弹性模型建立了双稳态复合材料层合结构的黏弹性模型，通过理论分析得到其第二稳态主曲率与扭曲率随加载时间和温度的变化关系。同时，利用有限元软件ABAQUS及其子程序UMAT建立了相应的有限元模型，研究了加载时间和温度对层合结构第二稳态性能的影响。理论与模拟结果均表明：层合结构第二稳态主曲率随加载时间的延长和温度的升高而增大；扭曲率随加载时间的延长而减小，一般情况下随温度的升高而增大，但在加载时间较长且温度较高时，可能会出现扭曲率随温度升高而减小的情况。理论计算结果与有限元模拟结果的比较显示两者吻合较好，可以通过有限元模拟对双稳态复合材料层合结构的黏弹性行为进行研究。 In order to ascertain the applications of bistable composite laminated structures in complicated environment, the viscoelastic behaviors of bistable composite laminated structures were investigated. The fiber was reduced to elastic material and the viscoelastic behaviors of matrix material were taken into consideration firstly. Then, based on the material properties of fiber and matrix, the viscoelastic material properties of the bistable composite laminated structure were obtained by theoretical analyses. A viscoelastic model of the bistable composite laminated structure was developed on the foundation of classical lamination theory, the principle of minimum potential energy and Maxwell viscoelasticity model, and the changing relationships between the second stable principal curvature, twist curvature and loading time, temperature were obtained by theoretical analyses. At the same time, the corresponding finite element model was developed using finite element software ABAQUS and its subroutine UMAT, and the influences of loading time and temperature on the second stable properties of laminated structures were investigated. Both of the theoretical and simulation results show that the second stable principal curvature of laminated structures increases with the loading time extension and temperature increasing. The twist curvature decreases with the loading time extension and increases with the temperature increasing in general case, but when the loading time is relatively long and the temperature is relatively high, may appear the circumstance of twist curvature decreases with the temperature increasing. The comparison of theoretical results and finite element simulation results show that both of them fit well, and it is feasible to investigate the viscoelastic behaviors of the bistable composite laminated structures by finite element simulation. 国家自然科学基金（51675485）；浙江省自然科学基金（LY15E050016）；高等学校博士学科点专项科研基金（20123317120003）