热超弹性材料中空穴增长的分岔问题

研究了受外加均布拉伸死载荷作用的不可压热超弹性材料中空穴突然快速增长的分岔问题.不同于外载荷较小的情况,不可压热超弹性材料球体中的预存微空在外载荷足够大时可以发生突然的快速增长,可视为一类分岔问题.给出了不同温度场下,不同初始半径的微空的增长曲线.预存微空的增长曲线相应于初始半径的极限是实心球体中空穴突然生成的分岔曲线.讨论了均匀和非均匀,升高或降低的温度场对空穴增长问题的影响;给出了预存微空能够发生突然的快速增长的临界载荷,得到了临界载荷与实心球体中空穴突然生成时的临界载荷之间的关系及临界载荷与温度变化之间的关系.

Bifurcation for Void Growth in Incompressible Thermo-Hyperelastic Materials

Bifurcation problem for sudden rapid growth of void in an incompressible thermo-hyperelastic sphere under radial uniform dead-load was examined.For sufficiently large values of load,the pre-existing void may get a sudden rapid growth contrary to that for small values of load.It may be seen as a kind of bifurcation problem.The growth curves of the void with different initial radius under different temperature fields were given.The limiting case for the growth of a micro-void corresponding to the initial radius is the cavitation bifurcation of a solid sphere.The effect of temperature change on the bifurcation was studied in the case of uniform and non-uniform temperature fields.The critical loads when the pre-existing void gets a sudden rapid growth were given.The relation curve between the critical load for the suddenly rapid growth and for the sudden formation of void was given.The relation curve between the critical load for suddenly rapid growth and the change of temperature was also given.