求解一类非线性粘弹性问题的弹性回复对应原理

本文提出了一个全新的粘弹性理论体系,它把传统的线粘弹性理论作为特殊情况包括在内。其主要结果是两个用于求解一类物理非线性粘弹性问题的弹性回复对应原理。利用它,只要知道相应的非线性弹性问题的解,就可以求出非线性粘弹性问题的解答。对应原理不是基于本构关系的相似性,而是基于从粘弹性现时响应到瞬时弹性响应的可回复性1]。首先找到非线性粘弹性与非线性弹性本构关系之间的对应,然后导出了两个弹性回复对应原理。通过对改性聚丙烯材料的实验验证了该对应原理的正确性和对此类材料的实用性。

ELASTICITY RECOVERY CORRESPONDENCE PRINCIPLE FOR SOLVING A CLASS OF NONLINEAR VISCOELASTIC PROBLEMS

A new theoretical system of viscoelasticity, which includes the traditional linear viscoelasticity as its special case, is proposed in this paper. The main results of this theory are two elasticity recovery correspondence principles, which are used for solving a class of physically nonlinear viscoelastic problems. By means of which, the solution of a nonlinear viscoelastic problem can be obtained if the solution of the corresponding nonlinear elastic problem is known. Correspondence principles are not based upon the similarity of the constitutive relations. Rather, they are based upon the recoverability from the present viscoelastic responses to the instantaneous elastic responses. The correspondence between the nonlinear viscoelastic and the nonlinear elastic constitutive relations is found first, and then two elasticity recovery correspondence principles are deduced. It is shown by the experiments for improved polypropylene that these principles are valid and are applicable to such class of materials.