集中力拉伸楔体大变形理论分析及数值计算

对任意向集中力拉伸用下的橡胶类材料楔体尖端应力应变场进行了渐近分析，并利用有限元与无限元耦合作了数值计算，结果表明大应变情况下，楔体尖端场处于单向拉伸状态，应力主奇异项为ｒ＾－λ，ｒ为变形后至顶点距离，λ依赖于材料本构常数，数值计算与理论解吻合很好。

THEORETICAL ANALYSIS AND NUMERICAL CALCULATION OF LARGE DEFORMATION FOR A WEDGE TENSIONED BY CONCENTRATED FORCE

As for the problem of large deformation, there are not many really important results.In 1973, Knowles and Sternberg gave a kind of constitutive relation for non-linear elasticity largedeformation and analyzed the elastic crack tip field. In 1990 and 1997, Gao gave two kinds ofconstitutive relations from different idea and analyzed many typical problems. In this paper, onekind of typical problem that is a rubber-like wedge tensioned by a concentrated force in arbitrarydirection is considered. Using the constitutive relation given by Gao in 1997 and proper mappingfunctions between before and after deformation, the problem is solved. The theoretical analysis isgiven and the results show that the wedge tip is in uni-axial state and the main stress term has the singularity of , in which r is the distance between an arbitrary point in the wedge andthe wedge tip point and A depends on the material constitutive constants, the other two stressterms are smaller than the main one. Furthermore, numerical calculation is done by means offinite element method. In order to describe the infinite boundary, infinite element is used to helpcalculation. The numerical results are consistent well with those of the theoretical analysis. Fromthe numerical results, it can be found that the wedge tip has the same direction as the externalforce no matter what direction the force is in.