中文摘要：

针对以往基于质点速度波形测量使用拉格朗日分析法反推材料动态力学性能时，需作某种简化假定或者必须同时实测应力边界，而在实验过程中的边界应力数据在某些情况下测不到或测不准的状况．因此基于路径线法和零初始条件，提出了一种改进的拉格朗日分析法，新方法可不涉及边界应力，直接反推出材料高应变率下的动态应力应变曲线．并且运用该方法对有机玻璃材料的动态性能进行了数值模拟研究分析，其结果与运用特征线法求得到的数据非常吻合，从而证实了该方法的可靠性和有效性．

英文摘要：

In the past, the data of boundary stress or a simplified assumption is essential for studying dynamic mechanical properties of materials using the Lagrangian analysis method based on the particle velocity wave-profiles measurements. However, the boundary stress data in some cases can not be detected or determined by the experimental measures. To tackle this situation, this paper presents a modified Lagrangian analysis method which does not involve the boundary stress computation. Starting from the path-lines method and utilizing the zero-initial condition, the material constitutive stress-strain curves under high strain-rates is deduced from only observing the particle velocity curve measurements. The dynamic stress/strain wave-profiles of the PMMA material, as a paradigm, are numerically studied using the proposed method, which are well in agreement with the theoretical result using the method of characteristics, which confirms the reliability and validity of the presented method.