橡胶楔体与刚性缺口接触大变形分析

利用Ｋｕｏｗｌｅｓ与Ｓｔｅｒｎｂｅｒｇ提出的非线性弹性大变形应变能函数，对橡胶楔体与刚性缺口接触问题进行大变形渐近分析，推导了楔体尖端场的渐近方程，得到楔体尖端附近的应力应变场及应力的奇异性指数与橡胶楔体角度、刚性缺口角度及材料常数有关的表达式；楔尖附近同一半径上应力分量为常数，同时，利用非线性有限元理论编制了大变形有限元程序，考虑楔体尖端与缺口接触边界条件，计算得到了与分析解一致的结论，当缺口角

LARGE DEFORMATION ANALYSIS OF A RUBBER WEDGE CONTACTING WITH A RIGID NOTCH

problem is very complex, especially, the contact problem oflarge deformation. When the contact surface contains vertex, the problemmust be solved by large strain theory. As for the large strain theory,the most important thing is to put out a reasonable and applicableconstitutive relation. In 1973, Knowles and Sternberg gave a kind ofconstitutive relation for non-linear elasticity large deformation andanalyzed the elastic crack tip field. In this paper, one kind of typicalproblem that is a rubber wedge contacting with a rigid notch isconsidered. Using the constitutive relation given by Knowles andSternberg in 1973 and proper mapping functions between before and afterdeformation, the problem is solved and the theoretical analysis is given.The results show that there is no expanding sector or shrinking sectornear the rubber wedge tip, not like the crack tip field in rubber-likematerial; When the rubber wedge is compressed into the rigid notch, thepoints on the same radius before deformation distribute evenly; Thedeformation in the direction of radius possesses singularity and thesingular exponent depends on the ratio of the rubber wedge angle to thenotch angle; The non-vanishing components of stress,τrr andτθθ, near the wedge tip possess the same singularity,r-2(n+1), and both componentsare independent of the angle after deformation. Furthermore, finiteelement program of large deformation is made and the contact boundaryconditions are added to the program, numerical calculation is done tothe typical contact problem. The numerical results are consistent wellwith those of the theoretical analysis.