摘要
在大变形超弹性理论框架下研究了内压、轴向拉伸和扭转联合作用下人体动脉壁的力学响应,应用结构不稳定性理论对动脉瘤生成的可能性进行了解释,应用材料强度理论对动脉瘤破裂的可能性进行了分析.考虑动脉壁中残余应力和平滑肌主动作用的影响,用纤维加强各向异性不可压超弹性复合材料两层厚壁圆筒模型来模拟动脉壁的力学特性.给出了正常和几种非正常状态下动脉壁的变形曲线和应力分布.变形和稳定性分析结果表明该文模型可以模拟正常状态下动脉壁的均匀变形,还可以模拟在动脉壁中弹性蛋白纤维和胶原蛋白纤维强度降低的非正常状态下动脉瘤生成的可能性及动脉瘤的增长.应力和强度分析结果表明该文模型可以模拟当动脉瘤中的最大应力超过管壁的强度时动脉瘤破裂的可能性.
Mechanical response of human arterial wall under the combined loading of inflation,axial extension and torsion was examined within the framework of the large deformation hyper-elastic theory.The probability for the formation of aneurysm was explained with the instability theory of structure and the probability for its rupture was explained with the strength theory of material.Taking account of the residual stress and the smooth muscle activity,a two layer thick-walled circular cylindrical tube model with fiber-reinforced composite-based incompressible anisotropic hyper-elastic materials was employed to model the mechanical behavior of the arterial wall.The deformation curves and the stress distributions of the arterial wall are given both under normal conditions and abnormal conditions.With the results of the deformation and the structure instability analysis,that not only the uniform inflation deformation of the arterial wall under normal conditions,but also the formation and growth of an aneurysm under abnormal conditions such as the stiffness of the elastic and collagen fibers is decreased to a certain degree may be described by this model.With the results of the stresses and the material strength analysis,that the rupture of aneurysm if the wall stress is larger than its strength may be described by this model,too.
出处
《应用数学和力学》
CSCD
北大核心
2010年第5期561-572,共12页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10772104
10872045)
上海市教委科研创新资助项目(09YZ12)
上海市重点学科建设资助项目(S30106)
关键词
蛋白纤维加强动脉壁
动脉瘤的生成和破裂
残余应力
结构不稳定性理论
材料强度理论
arterial wall with collagen fibers
formation and rupture of aneurysm
residual stress
instability theory of structure
strength theory of material
